messages listlengths 3 3 | topic stringclasses 1
value | subtopic stringclasses 3
values |
|---|---|---|
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.027 & 0.123 \\\\\n 0. & 0. \\\\\n 0.173 & 0.264 \\\\\n 0.787 & 0.039 \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.22 & 0.223 \\\\\n 0.427 & 0.183 \\\\\n 0.443 & 0.27 \\\\\n\\end{array}... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.225 & 0.099 \\\\\n 0.25 & 0.336 \\\\\n 0.258 & 0.716 \\\\\n 0.656 & 0.692 \\\\\n 0.67... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.039 & 0.739 \\\\\n 0.048 & 0.301 \\\\\n 0.209 & 0.957 \\\\\n 0.25 & 0.336 \\\\\n 0.37... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.006 & 0.719 \\\\\n 0. & 0. \\\\\n 0.25 & 0.049 \\\\\n 0.725 & 0.492 \\\\\n\\end{arra... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.047 & 0.465 \\\\\n 0.415 & 0.09 \\\\\n 0.417 & 0.824 \\\\\n 0.417 & 0.583 \\\\\n 0.43... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.407 & 0.524 \\\\\n 0. & 0. \\\\\n 0.072 & 0.065 \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.698 & 0.208 \\\\\n -0.52 & 0.037 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.2 & 0.407 \\\\\n 0.707 & 0.523 \\\\\n 0.723 & 0.704 \\\\\n\\end{array}\n\\right)$. Es... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.136 & 0.326 \\\\\n -0.011 & 0.876 \\\\\n 0. & 0. \\\\\n 0.112 & 0.88 \\\\\n 0.206 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.262 & 0.207 \\\\\n 0.458 & 0.272 \\\\\n 0.469 & 0.643 \\\\\n 0.587 & 0.663 \\\\\n 0.7... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.162 & 0.348 \\\\\n -0.127 & 0.217 \\\\\n 0. & 0. \\\\\n 0.247 & 0.331 \\\\\n\\end{ar... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.146 & 0.881 \\\\\n 0.253 & 0.621 \\\\\n 0.315 & 0.835 \\\\\n 0.36 & 0.474 \\\\\n\\end... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.305 & 0. \\\\\n 0. & 0. \\\\\n 0. & 0.208 \\\\\n 0.435 & 0.081 \\\\\n\\end{array}\n\... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.336 & 0.537 \\\\\n 0.375 & 0.027 \\\\\n 0.512 & 0.117 \\\\\n\\end{arra... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.29 & 0.152 \\\\\n 0.45 & 0.112 \\\\\n 0.459 & 0.721 \\\\\n 0.616 & 0.992 \\\\\n 0.763... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.569 & 0.555 \\\\\n -0.466 & 0.629 \\\\\n -0.377 & 0.073 \\\\\n -0.19 & 0.703 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.083 & 0.728 \\\\\n 0.085 & 0.257 \\\\\n 0.169 & 0.967 \\\\\n 0.412 & 0.255 \\\\\n 0.4... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.06 & 0.514 \\\\\n -0.055 & 0.58 \\\\\n 0. & 0. \\\\\n 0.123 & 0.794 \\\\\n 0.183 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.721 & 0.918 \\\\\n -0.655 & 0.526 \\\\\n -0.556 & 0.315 \\\\\n -0.378 & 0.799 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.02 & 0.981 \\\\\n 0.042 & 0.245 \\\\\n 0.197 & 0.887 \\\\\n 0.348 & 0.186 \\\\\n 0.71... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.578 & 0.258 \\\\\n -0.492 & 0.377 \\\\\n -0.202 & 0.438 \\\\\n -0.063 & 0.004 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.613 & 0.295 \\\\\n -0.459 & 0.779 \\\\\n -0.421 & 0.115 \\\\\n 0. & 0. \\\\\n\\end{a... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.075 & 0.304 \\\\\n 0. & 0. \\\\\n 0.111 & 0.043 \\\\\n 0.2 & 0.078 \\\\\n 0.332 & 0.... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.069 & 0.436 \\\\\n 0.387 & 0.567 \\\\\n 0.406 & 0.308 \\\\\n 0.44 & 0.264 \\\\\n 0.60... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.007 & 0.672 \\\\\n 0.522 & 0.215 \\\\\n 0.686 & 0.57 \\\\\n 0.802 & 0.717 \\\\\n 0.97... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.213 & 0.892 \\\\\n 0.3 & 0.672 \\\\\n 0.349 & 0.443 \\\\\n 0.409 & 0.779 \\\\\n 0.481... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.695 & 0.159 \\\\\n -0.291 & 0.226 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.107 & 0.153 \\\\\n -0.045 & 0.042 \\\\\n 0. & 0. \\\\\n 0.069 & 0.741 \\\\\n 0.164 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.204 & 0.715 \\\\\n 0.72 & 0.805 \\\\\n 0.772 & 0.383 \\\\\n\\end{array}\n\\right)$. E... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.466 & 0.174 \\\\\n -0.456 & 0.242 \\\\\n -0.414 & 0.093 \\\\\n -0.34 & 0.026 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.092 & 0.388 \\\\\n 0.228 & 0.207 \\\\\n 0.56 & 0.501 \\\\\n 0.648 & 0.214 \\\\\n 0.67... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.487 & 0.666 \\\\\n 0.887 & 0.843 \\\\\n 0.992 & 0.011 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.162 & 0.001 \\\\\n 0.321 & 0.402 \\\\\n 0.378 & 0.418 \\\\\n 0.558 & 0.634 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.025 & 0.958 \\\\\n 0.277 & 0.255 \\\\\n 0.328 & 0.01 \\\\\n 0.743 & 0.096 \\\\\n 0.80... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.323 & 0.141 \\\\\n -0.32 & 0.073 \\\\\n -0.281 & 0.755 \\\\\n -0.148 & 0.806 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.06 & 0.814 \\\\\n 0.17 & 0.318 \\\\\n 0.511 & 0.392 \\\\\n 0.577 & 0.221 \\\\\n 0.866... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.496 & 0.669 \\\\\n 0. & 0. \\\\\n 0.048 & 0.032 \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.033 & 0.181 \\\\\n 0.103 & 0.446 \\\\\n 0.326 & 0.993 \\\\\n 0.638 & 0.654 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.746 & 0.719 \\\\\n -0.63 & 0.419 \\\\\n -0.265 & 0.03 \\\\\n 0. & 0. \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.381 & 0.081 \\\\\n 0.662 & 0.998 \\\\\n 0.69 & 0.44 \\\\\n 0.933 & 0.838 \\\\\n\\end{... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.104 & 0.749 \\\\\n 0.379 & 0.97 \\\\\n 0.611 & 0.591 \\\\\n 0.943 & 0.356 \\\\\n\\end... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.43 & 0.735 \\\\\n -0.373 & 0.756 \\\\\n -0.277 & 0.436 \\\\\n -0.151 & 0.756 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.2 & 0.196 \\\\\n -0.2 & 0.349 \\\\\n -0.037 & 0.794 \\\\\n 0. & 0. \\\\\n 0.124 & 0.... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.003 & 0.565 \\\\\n 0.361 & 0.628 \\\\\n 0.361 & 0.409 \\\\\n 0.72 & 0.933 \\\\\n 0.95... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.138 & 0.301 \\\\\n 0.321 & 0.823 \\\\\n 0.389 & 0.996 \\\\\n 0.452 & 0.295 \\\\\n 0.7... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.904 & 0.195 \\\\\n -0.844 & 0.107 \\\\\n -0.714 & 0.646 \\\\\n -0.426 & 0.691 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.251 & 0.304 \\\\\n 0.282 & 0.888 \\\\\n 0.337 & 0.539 \\\\\n 0.497 & 0.77 \\\\\n 0.82... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.159 & 0.35 \\\\\n -0.115 & 0.183 \\\\\n 0. & 0. \\\\\n 0.148 & 0.073 \\\\\n 0.266 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.213 & 0.067 \\\\\n 0. & 0. \\\\\n 0.043 & 0.111 \\\\\n 0.148 & 0.462 \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.032 & 0.301 \\\\\n 0.138 & 0.466 \\\\\n 0.413 & 0.779 \\\\\n 0.643 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.233 & 0.54 \\\\\n -0.168 & 0.262 \\\\\n -0.005 & 0.691 \\\\\n 0. & 0. \\\\\n 0.08 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.366 & 0.098 \\\\\n -0.316 & 0.306 \\\\\n -0.246 & 0.545 \\\\\n -0.12 & 0.87 \\\\\n 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.231 & 0.52 \\\\\n -0.134 & 0.28 \\\\\n 0. & 0. \\\\\n 0.372 & 0.644 \\\\\n 0.393 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.134 & 0.238 \\\\\n 0.317 & 0.482 \\\\\n 0.486 & 0.071 \\\\\n 0.495 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.023 & 0.351 \\\\\n 0.084 & 0.43 \\\\\n 0.24 & 0.618 \\\\\n 0.258 & 0.121 \\\\\n 0.292... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.158 & 0.752 \\\\\n 0.179 & 0.517 \\\\\n 0.18 & 0.436 \\\\\n 0.38 & 0.068 \\\\\n 0.414... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.156 & 0.412 \\\\\n -0.078 & 0.637 \\\\\n 0. & 0. \\\\\n 0.287 & 0.83 \\\\\n 0.414 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.601 & 0.826 \\\\\n -0.595 & 0.591 \\\\\n -0.565 & 0.248 \\\\\n -0.495 & 0.06 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.305 & 0.065 \\\\\n 0.479 & 0.417 \\\\\n 0.773 & 0.135 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.748 & 0.366 \\\\\n -0.687 & 0.192 \\\\\n -0.576 & 0.625 \\\\\n -0.077 & 0.773 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.14 & 0.238 \\\\\n 0.187 & 0.153 \\\\\n 0.604 & 0.652 \\\\\n\\end{array}\n\\right)$. E... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.145 & 0.918 \\\\\n 0.28 & 0.022 \\\\\n 0.288 & 0.57 \\\\\n 0.324 & 0.884 \\\\\n 0.376... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.095 & 0.134 \\\\\n 0.668 & 0.069 \\\\\n 0.883 & 0.43 \\\\\n 0.926 & 0.923 \\\\\n\\end... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.545 & 0.052 \\\\\n -0.543 & 0.189 \\\\\n -0.443 & 0.572 \\\\\n -0.391 & 0.692 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.379 & 0.795 \\\\\n -0.373 & 0.427 \\\\\n 0. & 0. \\\\\n 0.555 & 0.28 \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.471 & 0.094 \\\\\n 0.509 & 0.304 \\\\\n 0.999 & 0.589 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.013 & 0.035 \\\\\n 0.345 & 0.151 \\\\\n 0.435 & 0.691 \\\\\n 0.479 & 0.159 \\\\\n 0.4... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.543 & 0.639 \\\\\n -0.363 & 0.315 \\\\\n -0.321 & 0.7 \\\\\n 0. & 0. \\\\\n 0.086 & ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.897 & 0.445 \\\\\n -0.864 & 0.555 \\\\\n -0.52 & 0.692 \\\\\n -0.502 & 0.043 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.303 & 0.184 \\\\\n 0.307 & 0.174 \\\\\n 0.34 & 0.505 \\\\\n 0.584 & 0.883 \\\\\n 0.69... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.272 & 0.847 \\\\\n 0.44 & 0.52 \\\\\n 0.638 & 0.42 \\\\\n 0.883 & 0.412 \\\\\n\\end{a... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.215 & 0.373 \\\\\n 0. & 0. \\\\\n 0.456 & 0.856 \\\\\n 0.703 & 0.453 \\\\\n\\end{arr... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.144 & 0.535 \\\\\n 0.374 & 0.216 \\\\\n 0.463 & 0.078 \\\\\n 0.468 & 0.396 \\\\\n 0.6... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.133 & 0.453 \\\\\n -0.108 & 0.752 \\\\\n 0. & 0. \\\\\n 0.007 & 0.792 \\\\\n 0.397 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.642 & 0.127 \\\\\n -0.63 & 0.339 \\\\\n -0.534 & 0.492 \\\\\n -0.446 & 0.606 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.344 & 0.669 \\\\\n -0.144 & 0.126 \\\\\n 0. & 0. \\\\\n 0.041 & 0.973 \\\\\n 0.098 &... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.018 & 0.699 \\\\\n 0.203 & 0.979 \\\\\n 0.27 & 0.766 \\\\\n 0.515 & 0.829 \\\\\n 0.60... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.228 & 0.306 \\\\\n 0.335 & 0.385 \\\\\n\\end{array}\n\\right)$. Estima... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.154 & 0.985 \\\\\n 0.224 & 0.08 \\\\\n 0.501 & 0.654 \\\\\n 0.772 & 0.245 \\\\\n 0.82... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.705 & 0.513 \\\\\n -0.498 & 0.049 \\\\\n -0.361 & 0.548 \\\\\n -0.25 & 0.002 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.353 & 0.238 \\\\\n -0.322 & 0.441 \\\\\n -0.303 & 0.459 \\\\\n -0.214 & 0.09 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $8$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.033 & 0.413 \\\\\n 0.269 & 0.409 \\\\\n 0.406 & 0.54 \\\\\n 0.448 & 0.505 \\\\\n 0.47... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.416 & 0.665 \\\\\n -0.148 & 0.476 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.325 & 0.139 \\\\\n -0.321 & 0.465 \\\\\n -0.253 & 0.644 \\\\\n -0.185 & 0.016 \\\\\n... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.119 & 0.001 \\\\\n 0.383 & 0.06 \\\\\n 0.729 & 0.16 \\\\\n\\end{array}\n\\right)$. Es... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.005 & 0.18 \\\\\n 0. & 0. \\\\\n 0.124 & 0.512 \\\\\n 0.332 & 0.164 \\\\\n 0.347 & 0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.478 & 0.924 \\\\\n 0.486 & 0.889 \\\\\n 0.827 & 0.846 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.02 & 0.49 \\\\\n 0.097 & 0.655 \\\\\n 0.362 & 0.064 \\\\\n 0.423 & 0.1... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.092 & 0.058 \\\\\n 0.149 & 0.718 \\\\\n 0.339 & 0.91 \\\\\n 0.978 & 0.073 \\\\\n\\end... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.965 & 0.642 \\\\\n -0.706 & 0.261 \\\\\n -0.67 & 0.666 \\\\\n -0.476 & 0.104 \\\\\n ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.397 & 0.151 \\\\\n -0.251 & 0.159 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.097 & 0.058 \\\\\n 0.165 & 0.493 \\\\\n 0.233 & 0.015 \\\\\n 0.248 & 0.118 \\\\\n 0.3... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.489 & 0.393 \\\\\n 0.555 & 0.684 \\\\\n 0.579 & 0.257 \\\\\n 0.909 & 0.85 \\\\\n\\end... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.37 & 0.374 \\\\\n -0.366 & 0.051 \\\\\n -0.287 & 0.543 \\\\\n -0.21 & 0.606 \\\\\n -... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.04 & 0.502 \\\\\n 0.186 & 0.406 \\\\\n 0.24 & 0.29 \\\\\n 0.462 & 0.035 \\\\\n 0.524 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.064 & 0.2 \\\\\n 0.258 & 0.393 \\\\\n 0.328 & 0.747 \\\\\n 0.394 & 0.625 \\\\\n 0.49 ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.39 & 0.809 \\\\\n -0.349 & 0.426 \\\\\n -0.343 & 0.892 \\\\\n -0.3 & 0.214 \\\\\n -0... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.129 & 0.63 \\\\\n 0.416 & 0.425 \\\\\n 0.898 & 0.96 \\\\\n\\end{array}\n\\right)$. Es... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.432 & 0.212 \\\\\n 0.499 & 0.129 \\\\\n 0.527 & 0.277 \\\\\n 0.667 & 0.838 \\\\\n\\en... | geometry | polygons |
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