messages listlengths 1 1 | ground_truth stringlengths 3 6 | dataset stringclasses 1 value |
|---|---|---|
[
{
"content": "SF = 7. J is placed 6 units away from F. Line W is the perpendicular bisector of segment JS. Point Q is the reflection of point F across line W. Point D is the midpoint of segment QJ. Let U be the midpoint of segment JS. Find the distance between points D and U. Express your answer as a decimal nu... | 3.0 | MATH |
[
{
"content": "Let US = 1. Line M is the perpendicular bisector of segment SU. Point X is the reflection of point S across point U. Point C is the reflection of point X across line M. Let J be the reflection of point C across point X. What is the distance between points C and J? Express your answer as a decimal ... | 6.0 | MATH |
[
{
"content": "HI = 4. Point A is obtained by rotating point H by angle pi/2 about point I. Let C be the rotation of point I by angle 7pi/12 around point A. Let W be the perpendicular bisector of segment IC. Line B passes through point C perpendicular to line W. Line X passes through point H parallel to line W. ... | 3.63 | MATH |
[
{
"content": "JS = 8. Line M passes through point J perpendicular to segment JS. Let Q be the reflection of point J across point S. Point C lies on line M at distance 11 from point S. Point H is the reflection of point C across segment JS. Let O be the perpendicular bisector of segment QC. Let E be the midpoint... | 6.86 | MATH |
[
{
"content": "Let HS = 8. Point K is obtained by rotating point H by angle 7pi/12 about point S. Point U is the reflection of point S across point K. Point X is obtained by rotating point U by angle 7pi/12 about point S. Point Y is the midpoint of segment XK. Line D passes through points K and Y. Line P is the ... | 104.98 | MATH |
[
{
"content": "Let VZ = 9. Let L be the rotation of point V by angle 5pi/6 around point Z. Point C is the reflection of point Z across point V. Point E is the midpoint of segment LV. Point P is the reflection of point Z across point L. Line W is the angle bisector of angle EPL. Point S is the reflection of point... | 19.53 | MATH |
[
{
"content": "SE = 2. Let L be the rotation of point S by angle pi/4 around point E. Let F be the rotation of point L by angle 5pi/12 around point S. Line Y passes through point S perpendicular to segment LF. Let N be the reflection of point E across point S. Point V is the midpoint of segment FN. Point G is th... | 2.8 | MATH |
[
{
"content": "Let EL = 8. J is placed 5 units away from L. Point R is obtained by rotating point J by angle 7pi/12 about point E. Let G be the reflection of point L across point J. Let M be the midpoint of segment GR. Let N be the reflection of point G across point R. Point U is the midpoint of segment LN. Let ... | 7.5 | MATH |
[
{
"content": "Let VJ = 7. Point Q is obtained by rotating point V by angle 5pi/6 about point J. Let H be the line through point J perpendicular to segment VQ. Let L be the midpoint of segment VQ. VI = 9. Let T be the rotation of point L by angle 5pi/6 around point V. Let A be the reflection of point I across po... | 26.12 | MATH |
[
{
"content": "Let OQ = 10. Point K is obtained by rotating point O by angle pi/6 about point Q. Let J be the reflection of point K across point O. Let W be the line through point K perpendicular to segment OK. Let C be the line through point O parallel to line W. Line N passes through points J and Q. Let V be t... | 6.94 | MATH |
[
{
"content": "AX = 1. Point J is the midpoint of segment XA. Let M be the rotation of point X by angle 7pi/12 around point A. Point E is the midpoint of segment XJ. Let C be the perpendicular bisector of segment XE. Let Q be the perpendicular bisector of segment AX. Let G be the reflection of line C across line... | 0.89 | MATH |
[
{
"content": "Let TB = 3. TG = 6. Point L is the midpoint of segment TB. Let S be the perpendicular bisector of segment BG. Point Q is the midpoint of segment BL. Let E be the line through point Q parallel to line S. Point W is the reflection of point L across line E. What is the distance between points W and Q... | 0.75 | MATH |
[
{
"content": "Let MJ = 12. Let F be the midpoint of segment MJ. Let V be the rotation of point M by angle 11pi/12 around point F. Let D be the midpoint of segment FV. Let K be the line through point V parallel to segment JM. Let O be the line through points D and F. Point I is the reflection of point F across p... | 6.4 | MATH |
[
{
"content": "Let MT = 8. Let G be the perpendicular bisector of segment TM. Point U is obtained by rotating point M by angle 2pi/3 about point T. Let X be the midpoint of segment UM. Point A is on line G. Point E is obtained by rotating point X by angle pi about point M. Let S be the angle bisector of angle EX... | 6.93 | MATH |
[
{
"content": "BD = 12. Point K is the midpoint of segment BD. Let J be the rotation of point B by angle 11pi/12 around point K. Line A passes through points J and D. Line E is the reflection of line A across point B. Let V be the line through point B perpendicular to line E. Let P be the line through point K pa... | 3.08 | MATH |
[
{
"content": "TJ = 12. Let I be the rotation of point J by angle 3pi/4 around point T. Line K passes through points I and T. Let R be the reflection of point I across point J. Let V be the reflection of line K through point J. Line L is the reflection of line V across point T. Let O be the midpoint of segment T... | 16.97 | MATH |
[
{
"content": "BW = 10. Let Z be the midpoint of segment WB. Let M be the rotation of point W by angle 3pi/4 around point Z. Let F be the angle bisector of angle MBZ. Point G is the midpoint of segment BM. Let P be the line through point G parallel to line F. Point X is the reflection of point G across point Z. ... | 12.28 | MATH |
[
{
"content": "TJ = 10. Line W is the perpendicular bisector of segment TJ. Point N is on line W with |NJ| = 2. Point C is the reflection of point J across point N. Point P is the midpoint of segment TC. Point S is the reflection of point P across segment TN. Point K is the intersection of segments SP and TN. Po... | 1.86 | MATH |
[
{
"content": "Let EY = 2. Point Q is obtained by rotating point Y by angle pi/2 about point E. Point L is the reflection of point Q across point Y. Let G be the midpoint of segment EQ. Let I be the midpoint of segment YG. Point D is obtained by rotating point Y by angle 2pi/3 about point L. Let X be the reflect... | 1.49 | MATH |
[
{
"content": "Let FP = 5. Line Q is the perpendicular bisector of segment PF. Point J is on line Q with |JP| = 5. Point H is the midpoint of segment FJ. Point X is the reflection of point H across point P. Let U be the midpoint of segment FX. Let O be the midpoint of segment PX. What is the length of segment UO... | 2.5 | MATH |
[
{
"content": "Let KT = 11. Point E is obtained by rotating point T by angle 2pi/3 about point K. Let D be the perpendicular bisector of segment KE. Let N be the midpoint of segment TE. Point U lies on line D. Let L be the midpoint of segment UN. Point R is the reflection of point L across line D. Find the dista... | 2.75 | MATH |
[
{
"content": "LK = 5. Let Q be the rotation of point K by angle 7pi/12 around point L. Let W be the rotation of point K by angle 3pi/4 around point Q. Let S be the rotation of point W by angle pi/12 around point Q. Point D is obtained by rotating point S by angle 5pi/12 about point L. Point J is the midpoint of... | 14.5 | MATH |
[
{
"content": "OR = 6. Let E be the reflection of point O across point R. Let M be the rotation of point O by angle pi/4 around point E. Let T be the midpoint of segment OR. Point Y is obtained by rotating point M by angle pi/2 about point T. Point H is the reflection of point Y across segment TM. Let S be the m... | 14.03 | MATH |
[
{
"content": "Let EO = 2. Point D is the midpoint of segment OE. Point S is obtained by rotating point E by angle 5pi/6 about point O. Point M is the reflection of point O across point E. Let K be the perpendicular bisector of segment OE. Let T be the reflection of point E across point M. Let V be the rotation ... | 64.58 | MATH |
[
{
"content": "KV = 11. Let Z be the rotation of point K by angle 11pi/12 around point V. Let S be the perpendicular bisector of segment ZV. Let B be the reflection of point V across point Z. Let P be the reflection of line S through point B. Let J be the angle bisector of angle VZK. Point A is the reflection of... | 60.55 | MATH |
[
{
"content": "XO = 5. Line B passes through points O and X. Let P be the reflection of point X across point O. Point W is the midpoint of segment OX. Point Z is the reflection of point W across point P. Line C passes through point X perpendicular to line B. Let E be the reflection of point Z across point X. Poi... | 12.1 | MATH |
[
{
"content": "DY = 1. Let B be the line through points Y and D. Let M be the reflection of point D across point Y. Point J is on line B. Point C is obtained by rotating point Y by angle pi/3 about point D. Let Q be the perpendicular bisector of segment MC. Point E is the reflection of point J across line Q. Lin... | 1.73 | MATH |
[
{
"content": "FU = 11. Line X passes through points F and U. Point E is the reflection of point U across point F. Point J is the reflection of point U across point E. Point D is on line X. Let Y be the perpendicular bisector of segment UF. Point B is on line Y. Point M is the midpoint of segment BD. Let V be th... | 16.5 | MATH |
[
{
"content": "WR = 3. Point H is the reflection of point R across point W. Point P is the reflection of point H across point R. Let J be the angle bisector of angle PRH. Line F passes through point H perpendicular to segment WP. Point C lies on line J. Point U is the reflection of point C across line F. Find th... | 12.0 | MATH |
[
{
"content": "Let XI = 4. Point G is obtained by rotating point X by angle 11pi/12 about point I. Point B is the reflection of point X across point I. Point W is the midpoint of segment BG. T is constructed so that GT = 4. Point C is the midpoint of segment XG. Line P passes through points G and T. Point O is t... | 2.99 | MATH |
[
{
"content": "Let HQ = 6. Let B be the midpoint of segment QH. Point G is the midpoint of segment QB. Let U be the line through points B and G. Point T is obtained by rotating point G by angle 7pi/12 about point Q. Let W be the perpendicular bisector of segment BT. Point N is the reflection of point B across po... | 1.28 | MATH |
[
{
"content": "LF = 6. Let J be the rotation of point F by angle 2pi/3 around point L. Let Q be the reflection of point F across point J. Line O passes through point Q parallel to segment LF. Let N be the line through point Q perpendicular to line O. Point T is the reflection of point F across line O. Point U is... | 43.27 | MATH |
[
{
"content": "RZ = 7. Let P be the rotation of point R by angle 5pi/12 around point Z. Point Q lies on segment ZP. Let X be the reflection of point Z across point R. Point J is the midpoint of segment ZP. Point G lies on segment XR. Let A be the midpoint of segment XR. Let T be the angle bisector of angle QGP. ... | 7.96 | MATH |
[
{
"content": "Let OH = 1. Let F be the reflection of point O across point H. Let T be the rotation of point F by angle pi/6 around point O. Let E be the vector from point T to point F. Let W be the midpoint of segment FT. Line S is the perpendicular bisector of segment FW. Point P is the reflection of point T a... | 0.46 | MATH |
[
{
"content": "Let HC = 2. Let Q be the vector from point C to point H. Let S be the perpendicular bisector of segment CH. Let G be the rotation of point H by angle 5pi/12 around point C. Let I be the rotation of point G by angle 5pi/6 around point H. Point J is the reflection of point I across line S. Let R be ... | 1.55 | MATH |
[
{
"content": "UE = 7. Let B be the line through points E and U. Point Z is on line B. Let A be the reflection of point Z across point U. Point F is the reflection of point A across point E. Find the distance between points F and Z. Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent ... | 14.0 | MATH |
[
{
"content": "UX = 5. Point S is obtained by rotating point X by angle 7pi/12 about point U. Point E is the reflection of point X across point U. Let V be the vector from point S to point U. Point Y is obtained by rotating point U by angle 11pi/12 about point E. Let Q be point U translated by vector V. Point J ... | 34.64 | MATH |
[
{
"content": "ES = 3. Line P passes through point S perpendicular to segment ES. Point L is the midpoint of segment SE. Point Y is the reflection of point L across line P. What is the distance between points Y and E? Express your answer as a decimal number rounded to 2 decimal places.\n\nPresent the answer in L... | 4.5 | MATH |
[
{
"content": "Let TB = 5. Let X be the reflection of point B across point T. Let D be the perpendicular bisector of segment BX. Point K is on line D with |KB| = 6. Point C is the reflection of point B across point X. Point J is the reflection of point T across segment KC. Let L be the midpoint of segment JX. Fi... | 5.19 | MATH |
[
{
"content": "Let LY = 3. Let Q be the perpendicular bisector of segment YL. Point B lies on line Q at distance 11 from point L. Let H be the reflection of point B across point Y. Point U is the midpoint of segment BY. Line F passes through points L and U. Point M is the reflection of point H across line Q. Lin... | 8.6 | MATH |
[
{
"content": "Let QY = 8. Let E be the perpendicular bisector of segment QY. Point J is the midpoint of segment QY. Point K is on line E with |KJ| = 12. Let L be the angle bisector of angle QYK. Let B be the midpoint of segment JK. Line S is the reflection of line L across point J. Let V be the midpoint of segm... | 14.36 | MATH |
[
{
"content": "Let WH = 2. Point O is obtained by rotating point H by angle 7pi/12 about point W. Line Y is the angle bisector of angle WHO. Line I is the perpendicular bisector of segment WO. Let F be the reflection of point W across point H. Line G is the reflection of line Y across point W. Point D is obtaine... | 6.85 | MATH |
[
{
"content": "LI = 4. Point Z is the reflection of point I across point L. Point A is obtained by rotating point L by angle 2pi/3 about point I. Line Y passes through point I perpendicular to segment LZ. Point F is the reflection of point Z across line Y. Let H be the perpendicular bisector of segment FL. Line ... | 6.74 | MATH |
[
{
"content": "GV = 3. Point B is the reflection of point G across point V. Let C be the reflection of point B across point G. Let J be the reflection of point G across point C. Let Z be the line through points J and C. Let H be the line through point B perpendicular to line Z. Point F is the midpoint of segment... | 35.25 | MATH |
[
{
"content": "Let AO = 5. Let B be the midpoint of segment AO. Point S is the midpoint of segment BA. Point U is obtained by rotating point A by angle 5pi/12 about point S. Let F be the reflection of point U across point O. Point W is the midpoint of segment UO. Let Z be the reflection of point A across point W... | 12.5 | MATH |
[
{
"content": "Let XO = 10. Let G be the reflection of point O across point X. Point B is the midpoint of segment XG. N is constructed so that BN = 3. Let L be the line through points O and B. Let Q be the reflection of point B across point N. Point W is on line L. Point F is the reflection of point Q across seg... | 0.75 | MATH |
[
{
"content": "EH = 12. Let T be the rotation of point H by angle pi/3 around point E. Point I is obtained by rotating point E by angle 3pi/4 about point T. Let Y be the line through points I and T. Line S is the reflection of line Y across point E. Point Z is the reflection of point E across line S. Point F is ... | 52.28 | MATH |
[
{
"content": "PN = 11. Point A is obtained by rotating point P by angle pi about point N. Point X is obtained by rotating point P by angle pi/12 about point N. Let I be the rotation of point P by angle pi/4 around point A. Point Q is the midpoint of segment AN. Line Z passes through point P perpendicular to seg... | 21.32 | MATH |
[
{
"content": "Let OT = 9. Let E be the midpoint of segment TO. Point G is obtained by rotating point E by angle pi/3 about point O. Let V be the angle bisector of angle OEG. Let Q be the reflection of point T across point G. Point X is the reflection of point Q across line V. Let I be the midpoint of segment EX... | 8.93 | MATH |
[
{
"content": "FA = 5. Let Y be the perpendicular bisector of segment FA. Let L be the reflection of point A across point F. Line B passes through point L parallel to line Y. Let G be the reflection of line Y across line B. Let S be the line through point A parallel to line G. Let J be the perpendicular bisector... | 7.5 | MATH |
[
{
"content": "FN = 6. Point L is obtained by rotating point N by angle 11pi/12 about point F. Line R is the angle bisector of angle LNF. Point S is obtained by rotating point N by angle 5pi/6 about point F. Let E be the rotation of point S by angle pi/2 around point N. Let A be the midpoint of segment FE. Let T... | 7.93 | MATH |
[
{
"content": "UA = 4. Let L be the vector from point U to point A. Point R is the reflection of point U across point A. Line T is the perpendicular bisector of segment RA. Point H is the midpoint of segment AU. Line W is the reflection of line T across point A. Line S is the perpendicular bisector of segment UH... | 14.73 | MATH |
[
{
"content": "PM = 3. Let Q be the rotation of point P by angle pi/2 around point M. Point Z is the reflection of point Q across point P. Let O be the midpoint of segment ZM. Let T be the reflection of point P across point Z. Point U is the midpoint of segment MT. Find the length of segment UO. Express your ans... | 2.12 | MATH |
[
{
"content": "Let EI = 1. Let K be the midpoint of segment EI. Point M is obtained by rotating point K by angle 5pi/6 about point I. Point L is the reflection of point I across point M. Let Q be the reflection of point M across point K. Let G be the vector from point I to point Q. Point N is the translation of ... | 1.7 | MATH |
[
{
"content": "GS = 7. Point D is obtained by rotating point G by angle 5pi/6 about point S. Point O is the reflection of point D across point G. Point V is obtained by rotating point S by angle 11pi/12 about point O. Let J be the angle bisector of angle DOV. Point P is the midpoint of segment GO. Point W is the... | 26.95 | MATH |
[
{
"content": "Let HL = 8. Let E be the midpoint of segment LH. Let T be the reflection of point E across point L. Point N is the reflection of point H across point T. Let B be the line through point E perpendicular to segment LH. Let Y be the midpoint of segment NE. Line S is the reflection of line B across poi... | 22.0 | MATH |
[
{
"content": "Let ML = 12. Let X be the rotation of point M by angle 5pi/6 around point L. Point V is obtained by rotating point X by angle 3pi/4 about point M. Point Z is the reflection of point M across point L. Line B is the angle bisector of angle LMX. Line W is the reflection of line B across point X. Let ... | 19.06 | MATH |
[
{
"content": "Let GH = 3. Line X is the perpendicular bisector of segment HG. Let U be the reflection of point H across point G. Point O is the midpoint of segment UG. Point E is the reflection of point H across point U. Let S be the rotation of point O by angle 5pi/6 around point U. Let P be the perpendicular ... | 17.63 | MATH |
[
{
"content": "Let OD = 6. Let U be the rotation of point O by angle pi/6 around point D. Let G be the midpoint of segment DO. Point Z is the reflection of point G across point U. Let N be the midpoint of segment OZ. Line X is the angle bisector of angle DZG. Let Y be the rotation of point Z by angle 7pi/12 arou... | 5.02 | MATH |
[
{
"content": "GX = 1. Point Q is the midpoint of segment GX. Let B be the reflection of point G across point X. Line V passes through point B perpendicular to segment GX. Point Z is the reflection of point G across line V. Let M be the reflection of point G across point Z. Point K is obtained by rotating point ... | 0.63 | MATH |
[
{
"content": "Let XN = 1. Let R be the reflection of point N across point X. Let I be the perpendicular bisector of segment NR. Point C is on line I with |CX| = 5. Let F be the midpoint of segment XR. Line V is the angle bisector of angle NRC. Let A be the reflection of point N across point F. Let S be the refl... | 13.43 | MATH |
[
{
"content": "HN = 9. Line E is the perpendicular bisector of segment NH. Let V be the line through point H parallel to line E. Let S be the midpoint of segment NH. Point P lies on line V at distance 12 from point N. Point Z is the midpoint of segment NP. Let A be the reflection of point Z across point S. Point... | 9.28 | MATH |
[
{
"content": "QE = 3. Let T be the rotation of point Q by angle pi/3 around point E. Let A be the vector from point T to point Q. Let F be the midpoint of segment TQ. Let D be the rotation of point F by angle 3pi/4 around point E. Let O be point D translated by vector A. Let V be the midpoint of segment TO. Lin... | 8.8 | MATH |
[
{
"content": "Let QT = 12. Point Y is the reflection of point Q across point T. Line X passes through points Y and Q. Let M be the angle bisector of angle YTQ. Let F be the line through point Q perpendicular to line X. Point J is the reflection of point T across line F. Point V is the reflection of point J acro... | 48.0 | MATH |
[
{
"content": "UV = 2. Let Y be the rotation of point V by angle pi/3 around point U. Point X is the midpoint of segment YU. Point G is the midpoint of segment VX. Let W be the reflection of point Y across point G. Point P is the reflection of point W across segment UV. Let O be the midpoint of segment GW. Let F... | 1.41 | MATH |
[
{
"content": "Let WQ = 5. Let T be the rotation of point W by angle pi/4 around point Q. Let H be the midpoint of segment QW. Point X is the midpoint of segment WH. Point F is the reflection of point T across point H. Point C is the midpoint of segment FX. What is the length of segment CT? Express your answer a... | 5.38 | MATH |
[
{
"content": "Let RD = 9. Point J is obtained by rotating point R by angle 7pi/12 about point D. Point B is the midpoint of segment RJ. Let T be the rotation of point R by angle 7pi/12 around point B. Line M passes through points D and T. Point H is the reflection of point B across line M. Let V be the line thr... | 8.18 | MATH |
[
{
"content": "Let UT = 2. Point J is the midpoint of segment UT. Point A is the reflection of point U across point T. Let R be the rotation of point U by angle pi/3 around point J. Let S be the rotation of point J by angle 2pi/3 around point A. Let Y be the perpendicular bisector of segment UT. Line M is the an... | 1.39 | MATH |
[
{
"content": "Let UN = 9. Point D is obtained by rotating point U by angle 2pi/3 about point N. Let E be the midpoint of segment NU. Line C is the perpendicular bisector of segment NU. Point M lies on segment NU. Let H be the reflection of point D across point E. Let P be the rotation of point U by angle pi/4 a... | 19.69 | MATH |
[
{
"content": "YE = 6. Point H is the reflection of point Y across point E. Let O be the midpoint of segment YE. Let Q be the reflection of point H across point O. Point G is the midpoint of segment QO. What is the distance between points G and Q? Express your answer as a decimal number rounded to 2 decimal plac... | 4.5 | MATH |
[
{
"content": "TL = 3. Let Q be the midpoint of segment LT. Let Z be the perpendicular bisector of segment TQ. Point E is on line Z with |ET| = 2. Let R be the reflection of point Q across point L. Point C is the reflection of point R across point Q. Let G be the midpoint of segment RE. Point M is the reflection... | 8.49 | MATH |
[
{
"content": "LQ = 3. Let I be the vector from point Q to point L. Point X is the midpoint of segment QL. Point W is the translation of point X by vector I. Let O be the rotation of point X by angle pi/3 around point L. Let Y be the midpoint of segment OQ. Let B be the perpendicular bisector of segment OY. Line... | 3.16 | MATH |
[
{
"content": "US = 3. Point Q is the reflection of point U across point S. Let P be the rotation of point U by angle 11pi/12 around point S. Let W be the vector from point P to point S. Line A passes through points U and S. Let L be the vector from point S to point Q. Point J lies on line A. Let Z be point S tr... | 8.54 | MATH |
[
{
"content": "Let WF = 3. Point X is obtained by rotating point W by angle 7pi/12 about point F. Point R is the midpoint of segment XF. Let N be the vector from point X to point R. Let B be the angle bisector of angle WFX. Point Y is the reflection of point X across point W. Line A passes through points Y and R... | 10.62 | MATH |
[
{
"content": "Let KH = 1. Let V be the midpoint of segment KH. Point Y is the reflection of point H across point K. Let R be the rotation of point Y by angle pi/3 around point V. Point S is the reflection of point V across point H. Line W is the perpendicular bisector of segment YS. Line O is the reflection of ... | 1.32 | MATH |
[
{
"content": "FK = 3. Line J passes through points K and F. Let Y be the rotation of point F by angle 3pi/4 around point K. Let S be the line through point K perpendicular to line J. Line A is the reflection of line S across point F. Point V is the reflection of point Y across line A. Point M is the reflection ... | 8.39 | MATH |
[
{
"content": "Let ET = 11. Let F be the rotation of point T by angle 2pi/3 around point E. Point O is the midpoint of segment FT. Line B is the perpendicular bisector of segment FT. Point A is the midpoint of segment EO. Point U is obtained by rotating point E by angle pi/4 about point A. Point G is obtained by... | 24.14 | MATH |
[
{
"content": "MP = 3. Let D be the vector from point M to point P. Let G be the rotation of point P by angle pi/3 around point M. Point C is the reflection of point G across segment MP. Point W is the translation of point C by vector D. Let E be the rotation of point P by angle 5pi/6 around point M. Let A be th... | 18.33 | MATH |
[
{
"content": "Let DP = 3. Point U is the reflection of point D across point P. Let L be the line through points D and U. Let S be the line through point D perpendicular to line L. Point H is the reflection of point P across line S. What is the distance between points H and D? Express your answer as a decimal nu... | 3.0 | MATH |
[
{
"content": "UR = 3. Point E is obtained by rotating point U by angle 5pi/6 about point R. Point Z is the midpoint of segment UE. Let A be the perpendicular bisector of segment UR. Point N is the midpoint of segment UR. Let X be the line through point Z parallel to segment UR. Let P be the reflection of point ... | 5.44 | MATH |
[
{
"content": "XM = 6. Let L be the rotation of point M by angle pi/4 around point X. Let Q be the midpoint of segment LX. Let N be the line through point Q perpendicular to segment MX. Point P is the reflection of point L across line N. Let T be the midpoint of segment MX. Find the distance between points T and... | 5.2 | MATH |
[
{
"content": "UK = 9. Let V be the reflection of point U across point K. Let Q be the reflection of point V across point U. Point E is the reflection of point K across point V. Point N is obtained by rotating point V by angle 7pi/12 about point E. Let R be the midpoint of segment QK. Let J be the perpendicular ... | 76.79 | MATH |
[
{
"content": "Let KP = 7. Let B be the perpendicular bisector of segment PK. Let U be the reflection of line B through point P. Point Q is the reflection of point K across point P. Line E is the reflection of line B across line U. Point C lies on segment PK. Line I passes through point K perpendicular to segmen... | 87.5 | MATH |
[
{
"content": "Let KL = 6. Let P be the midpoint of segment KL. Let U be the perpendicular bisector of segment KL. Let N be the reflection of point L across point K. Point R is on line U with |RP| = 6. Let O be the reflection of point R across point N. Let I be the midpoint of segment PL. Let G be the midpoint o... | 38.25 | MATH |
[
{
"content": "EN = 12. Let M be the reflection of point E across point N. Let J be the rotation of point M by angle 3pi/4 around point N. Let W be the midpoint of segment JN. Point Y is the midpoint of segment WM. Point B is the reflection of point E across point Y. Point O is the midpoint of segment NB. Point ... | 6.0 | MATH |
[
{
"content": "Let VP = 4. Let H be the rotation of point V by angle pi/3 around point P. Let Q be the midpoint of segment HV. Let L be the midpoint of segment PQ. Let J be the perpendicular bisector of segment HP. Let R be the reflection of line J through point L. Point A is the midpoint of segment HP. Let E be... | 18.61 | MATH |
[
{
"content": "ES = 3. Line U is the perpendicular bisector of segment ES. Let K be the line through point S parallel to line U. Let B be the reflection of line K across line U. Line Z is the reflection of line B across point S. Point C lies on line B at distance 8 from point E. Let L be the midpoint of segment ... | 12.09 | MATH |
[
{
"content": "GA = 9. Let D be the midpoint of segment GA. Let S be the rotation of point D by angle 3pi/4 around point A. Let J be the reflection of point S across point D. Let V be the perpendicular bisector of segment AS. Line N is the perpendicular bisector of segment DS. Let W be the line through point J p... | 15.48 | MATH |
[
{
"content": "Let WO = 5. Let D be the reflection of point O across point W. Point R is obtained by rotating point W by angle 5pi/6 about point D. Point Y is the reflection of point R across point D. Point H is the reflection of point D across point Y. Point T is the reflection of point W across point H. Point ... | 10.0 | MATH |
[
{
"content": "Let DY = 4. Let B be the midpoint of segment YD. Let T be the rotation of point Y by angle 5pi/6 around point B. Let N be the perpendicular bisector of segment DY. Let S be the rotation of point B by angle pi/3 around point Y. Point K is the reflection of point S across line N. Let Q be the reflec... | 4.26 | MATH |
[
{
"content": "LI = 11. Let D be the reflection of point L across point I. Point X is the midpoint of segment LI. Let A be the rotation of point D by angle 2pi/3 around point L. Point O is obtained by rotating point D by angle pi about point A. Let T be the line through point O perpendicular to segment LI. Point... | 100.37 | MATH |
[
{
"content": "Let LP = 12. Point N is obtained by rotating point P by angle pi/12 about point L. Let I be the rotation of point P by angle pi/2 around point L. Let T be the midpoint of segment LP. Point U is the reflection of point T across segment PI. Point R is the reflection of point U across segment LP. Fin... | 9.12 | MATH |
[
{
"content": "Let PI = 10. Line W passes through point P perpendicular to segment IP. Point H is the reflection of point I across line W. Let Q be the reflection of line W through point I. Point R is the reflection of point H across line Q. Find the distance between points H and R. Express your answer as a deci... | 60.0 | MATH |
[
{
"content": "Let GO = 2. Let S be the reflection of point G across point O. Let C be the line through points S and G. Point Y is obtained by rotating point S by angle pi/12 about point G. Let B be the angle bisector of angle SOY. Let Z be the line through point O perpendicular to line C. Let V be the reflectio... | 0.25 | MATH |
[
{
"content": "JR = 6. Z is placed 11 units away from R. Line D passes through points R and Z. Let W be the midpoint of segment RZ. Let N be the vector from point Z to point W. Point X is obtained by rotating point Z by angle 11pi/12 about point W. Let F be point R translated by vector N. Point S is the reflecti... | 21.28 | MATH |
[
{
"content": "Let HN = 5. Point I is the midpoint of segment NH. Line G is the angle bisector of angle HIN. Line S is the perpendicular bisector of segment IN. Point V is the reflection of point I across point N. Point R is on line S with |RN| = 5. Let Q be the reflection of point H across point R. Point U is t... | 16.01 | MATH |
[
{
"content": "Let HF = 1. Let X be the midpoint of segment FH. Let M be the midpoint of segment XH. Let L be the perpendicular bisector of segment MX. Point K is on line L with |KM| = 2. Point B is the midpoint of segment KH. Let N be the line through point B parallel to line L. Point Y is the reflection of poi... | 0.88 | MATH |
[
{
"content": "LX = 11. Point T is obtained by rotating point X by angle 7pi/12 about point L. Let W be the vector from point T to point L. Let K be point X translated by vector W. Point O is obtained by rotating point L by angle 3pi/4 about point T. Let Z be the angle bisector of angle TXL. Let G be the rotatio... | 70.77 | MATH |
[
{
"content": "HM = 8. Point D is obtained by rotating point M by angle pi/4 about point H. Let V be the vector from point M to point H. Let U be point D translated by vector V. Let I be the midpoint of segment HU. Point O is the reflection of point U across point D. Let Z be the reflection of point O across poi... | 20.0 | MATH |
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