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 $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.069 & 0.952 \\\\\n 0.141 & 0.696 \\\\\n 0.259 & 0.086 \\\\\n 0.325 & 0.378 \\\\\n 0.5... | 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 0.11 & 0.821 \\\\\n 0.314 & 0.241 \\\\\n 0.628 & 0.379 \\\\\n 0.735 & 0.966 \\\\\n\\end... | 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 0.009 & 0.099 \\\\\n 0.01 & 0.124 \\\\\n 0.076 & 0.388 \\\\\n 0.14 & 0.955 \\\\\n 0.81 ... | 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 0.136 & 0.854 \\\\\n 0.502 & 0.692 \\\\\n 0.849 & 0.812 \\\\\n 0.887 & 0.899 \\\\\n\\en... | 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 -0.448 & 0.293 \\\\\n -0.389 & 0.358 \\\\\n -0.117 & 0.586 \\\\\n 0. & 0. \\\\\n 0.01 &... | 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 -0.225 & 0.415 \\\\\n -0.177 & 0.945 \\\\\n -0.172 & 0.066 \\\\\n 0. & 0. \\\\\n 0.243 ... | 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 -0.232 & 0.018 \\\\\n -0.197 & 0.505 \\\\\n -0.184 & 0.645 \\\\\n -0.124 & 0.772 \\\\\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 -0.257 & 0.284 \\\\\n 0. & 0. \\\\\n 0.135 & 0.009 \\\\\n 0.433 & 0.041 \\\\\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 -0.159 & 0.147 \\\\\n 0. & 0. \\\\\n 0.112 & 0.536 \\\\\n 0.48 & 0.638 \\\\\n\\end{arra... | 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 -0.35 & 0.403 \\\\\n -0.35 & 0.348 \\\\\n -0.306 & 0.71 \\\\\n -0.004 & 0.772 \\\\\n 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 0.051 & 0.692 \\\\\n 0.201 & 0.291 \\\\\n 0.437 & 0.39 \\\\\n 0.521 & 0.348 \\\\\n 0.58... | 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 0.111 & 0.32 \\\\\n 0.153 & 0.699 \\\\\n 0.672 & 0.603 \\\\\n 0.806 & 0.427 \\\\\n\\end... | 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 $\\left(\n\\begin{array}{cc}\n -0.77 & 0.721 \\\\\n -0.365 & 0.323 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.431 & 0.33 \\\\\n -0.419 & 0.243 \\\\\n -0.322 & 0.489 \\\\\n -0.267 & 0.522 \\\\\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 0.145 & 0.216 \\\\\n 0.384 & 0.844 \\\\\n 0.483 & 0.451 \\\\\n 0.588 & 0.967 \\\\\n 0.6... | 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 -0.359 & 0.291 \\\\\n -0.337 & 0.153 \\\\\n -0.229 & 0.677 \\\\\n 0. & 0. \\\\\n 0.133 ... | 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 0.101 & 0.365 \\\\\n 0.127 & 0.718 \\\\\n 0.258 & 0.673 \\\\\n 0.282 & 0.933 \\\\\n 0.3... | 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 0.453 & 0.837 \\\\\n 0.454 & 0.617 \\\\\n 0.543 & 0.744 \\\\\n 0.593 & 0.168 \\\\\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 0.001 & 0.088 \\\\\n 0.152 & 0.023 \\\\\n 0.259 & 0.902 \\\\\n 0.78 & 0.598 \\\\\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 -0.302 & 0.005 \\\\\n 0. & 0. \\\\\n 0.059 & 0.073 \\\\\n 0.112 & 0.188 \\\\\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 0.258 & 0.673 \\\\\n 0.574 & 0.604 \\\\\n 0.707 & 0.978 \\\\\n 0.961 & 0.092 \\\\\n\\en... | 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 $\\left(\n\\begin{array}{cc}\n -0.712 & 0.185 \\\\\n -0.119 & 0.411 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.651 & 0.25 \\\\\n -0.499 & 0.045 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. 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 $\\left(\n\\begin{array}{cc}\n -0.123 & 0.002 \\\\\n -0.076 & 0.216 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.531 & 0.114 \\\\\n -0.413 & 0.535 \\\\\n -0.03 & 0.437 \\\\\n 0. & 0. \\\\\n\\end{ar... | 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 $\\left(\n\\begin{array}{cc}\n 0.251 & 0.689 \\\\\n 0.557 & 0.665 \\\\\n 0.807 & 0.572 \\\\\n\\end{array}\n\\right)$. ... | 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. & 0. \\\\\n 0.001 & 0.208 \\\\\n 0.026 & 0.436 \\\\\n 0.151 & 0.656 \\\\\n 0.239 & 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 -0.096 & 0.063 \\\\\n 0. & 0. \\\\\n 0.024 & 0.631 \\\\\n 0.15 & 0.777 \\\\\n 0.256 & 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 0.054 & 0.667 \\\\\n 0.068 & 0.195 \\\\\n 0.117 & 0.086 \\\\\n 0.372 & 0.689 \\\\\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. & 0. \\\\\n 0.069 & 0.045 \\\\\n 0.206 & 0.735 \\\\\n 0.247 & 0.79 \\\\\n\\end{array... | 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 $\\left(\n\\begin{array}{cc}\n -0.293 & 0.285 \\\\\n -0.062 & 0.298 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.499 & 0.824 \\\\\n -0.446 & 0.2 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Estima... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.129 & 0.088 \\\\\n 0.209 & 0.811 \\\\\n 0.25 & 0.151 \\\\\n 0.443 & 0.015 \\\\\n 0.59... | 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 0.109 & 0.136 \\\\\n 0.336 & 0.178 \\\\\n 0.336 & 0.49 \\\\\n 0.448 & 0.893 \\\\\n 0.54... | 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 $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.212 & 0.288 \\\\\n 0.56 & 0.442 \\\\\n\\end{array}\n\\right)$. Estimat... | 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 -0.385 & 0.137 \\\\\n -0.048 & 0.66 \\\\\n 0. & 0. \\\\\n 0.22 & 0.623 \\\\\n 0.223 & 0... | 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 0.469 & 0.186 \\\\\n 0.747 & 0.195 \\\\\n 0.967 & 0.129 \\\\\n\\end{arra... | 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 $\\left(\n\\begin{array}{cc}\n 0.127 & 0.257 \\\\\n 0.363 & 0.677 \\\\\n 0.588 & 0.682 \\\\\n\\end{array}\n\\right)$. ... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.441 & 0.294 \\\\\n 0. & 0. \\\\\n 0.221 & 0.265 \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $9$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.08 & 0.802 \\\\\n 0. & 0. \\\\\n 0.025 & 0.862 \\\\\n 0.039 & 0.007 \\\\\n 0.075 & 0... | 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 0.47 & 0.509 \\\\\n 0.573 & 0.397 \\\\\n 0.614 & 0.208 \\\\\n 0.963 & 0.899 \\\\\n\\end... | 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 $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.293 & 0.634 \\\\\n 0.587 & 0.742 \\\\\n\\end{array}\n\\right)$. Estima... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.269 & 0.043 \\\\\n 0.481 & 0.395 \\\\\n 0.786 & 0.269 \\\\\n 0.91 & 0.533 \\\\\n\\end... | 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 0.076 & 0.141 \\\\\n 0.125 & 0.602 \\\\\n 0.211 & 0.152 \\\\\n 0.737 & 0.795 \\\\\n 0.8... | 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 -0.425 & 0.143 \\\\\n -0.288 & 0.048 \\\\\n -0.168 & 0.02 \\\\\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 $3$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.796 & 0.199 \\\\\n -0.222 & 0.628 \\\\\n 0. & 0. \\\\\n\\end{array}\n\\right)$. Esti... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.423 & 0.915 \\\\\n 0.436 & 0.023 \\\\\n 0.622 & 0.215 \\\\\n 0.76 & 0.565 \\\\\n\\end... | 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 0.161 & 0.742 \\\\\n 0.446 & 0.159 \\\\\n 0.449 & 0.972 \\\\\n 0.509 & 0.055 \\\\\n 0.5... | 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 -0.66 & 0.04 \\\\\n -0.583 & 0.248 \\\\\n -0.442 & 0.535 \\\\\n -0.249 & 0.003 \\\\\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 -0.261 & 0.47 \\\\\n -0.221 & 0.112 \\\\\n -0.198 & 0.04 \\\\\n -0.159 & 0.005 \\\\\n 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 -0.006 & 0.089 \\\\\n 0. & 0. \\\\\n 0. & 0.579 \\\\\n 0.063 & 0.741 \\\\\n 0.577 & 0.0... | 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 $\\left(\n\\begin{array}{cc}\n 0. & 0. \\\\\n 0.424 & 0.516 \\\\\n 0.746 & 0.419 \\\\\n\\end{array}\n\\right)$. 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 0.414 & 0.019 \\\\\n 0.583 & 0.412 \\\\\n 0.699 & 0.836 \\\\\n 0.734 & 0.554 \\\\\n 0.8... | 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 0.207 & 0.548 \\\\\n 0.231 & 0.046 \\\\\n 0.265 & 0.786 \\\\\n 0.755 & 0.294 \\\\\n\\en... | 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 -0.277 & 0.335 \\\\\n -0.263 & 0.715 \\\\\n -0.222 & 0.022 \\\\\n -0.151 & 0.731 \\\\\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 0.041 & 0.226 \\\\\n 0.064 & 0.01 \\\\\n 0.319 & 0.389 \\\\\n 0.886 & 0.037 \\\\\n 0.94... | 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 $\\left(\n\\begin{array}{cc}\n 0.842 & 0.023 \\\\\n 0.847 & 0.704 \\\\\n 0.911 & 0.046 \\\\\n\\end{array}\n\\right)$. ... | 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 0.105 & 0.849 \\\\\n 0.223 & 0.387 \\\\\n 0.255 & 0.61 \\\\\n 0.729 & 0.414 \\\\\n 0.76... | 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 0.014 & 0.729 \\\\\n 0.122 & 0.306 \\\\\n 0.305 & 0.02 \\\\\n 0.482 & 0.842 \\\\\n 0.71... | 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 0.139 & 0.181 \\\\\n 0.206 & 0.662 \\\\\n 0.223 & 0.252 \\\\\n 0.556 & 0.426 \\\\\n 0.5... | 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 0.566 & 0.915 \\\\\n 0.609 & 0.648 \\\\\n 0.753 & 0.447 \\\\\n 0.778 & 0.586 \\\\\n 0.8... | 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 0.03 & 0.186 \\\\\n 0.123 & 0.658 \\\\\n 0.194 & 0.947 \\\\\n 0.494 & 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 -0.264 & 0.268 \\\\\n 0. & 0. \\\\\n 0.215 & 0.65 \\\\\n 0.238 & 0.018 \\\\\n 0.556 & 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 0.429 & 0.557 \\\\\n 0.724 & 0.75 \\\\\n 0.745 & 0.675 \\\\\n 0.792 & 0.991 \\\\\n 0.96... | 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 -0.32 & 0.032 \\\\\n -0.317 & 0.329 \\\\\n -0.206 & 0.807 \\\\\n 0. & 0. \\\\\n 0.227 &... | 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 0.143 & 0.553 \\\\\n 0.195 & 0.969 \\\\\n 0.386 & 0.15 \\\\\n 0.767 & 0.864 \\\\\n 0.81... | 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 & 0.701 \\\\\n 0.041 & 0.049 \\\\\n 0.288 & 0.391 \\\\\n 0.462 & 0.063 \\\\\n 0.5... | 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. & 0. \\\\\n 0.065 & 0.318 \\\\\n 0.098 & 0.438 \\\\\n 0.277 & 0.567 \\\\\n 0.425 & 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 $\\left(\n\\begin{array}{cc}\n 0.225 & 0.099 \\\\\n 0.625 & 0.85 \\\\\n 0.747 & 0.965 \\\\\n\\end{array}\n\\right)$. E... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.053 & 0.935 \\\\\n 0.537 & 0.245 \\\\\n 0.869 & 0.377 \\\\\n 0.921 & 0.791 \\\\\n\\en... | 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 -0.561 & 0.222 \\\\\n -0.553 & 0.453 \\\\\n 0. & 0. \\\\\n 0.089 & 0.523 \\\\\n 0.216 &... | 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 0.075 & 0.838 \\\\\n 0.684 & 0.691 \\\\\n 0.789 & 0.394 \\\\\n 0.98 & 0.451 \\\\\n\\end... | 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 -0.849 & 0.196 \\\\\n -0.686 & 0.792 \\\\\n -0.543 & 0.904 \\\\\n -0.299 & 0.904 \\\\\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 $\\left(\n\\begin{array}{cc}\n -0.097 & 0.667 \\\\\n 0. & 0. \\\\\n 0.092 & 0.034 \\\\\n\\end{array}\n\\right)$. Estim... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $7$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.042 & 0.605 \\\\\n 0.178 & 0.738 \\\\\n 0.195 & 0.124 \\\\\n 0.551 & 0.682 \\\\\n 0.5... | 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 0.034 & 0.284 \\\\\n 0.122 & 0.146 \\\\\n 0.179 & 0.683 \\\\\n 0.209 & 0.327 \\\\\n 0.2... | 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 -0.322 & 0.4 \\\\\n -0.206 & 0.004 \\\\\n 0. & 0. \\\\\n 0.36 & 0.029 \\\\\n\\end{array... | 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 -0.235 & 0.093 \\\\\n 0. & 0. \\\\\n 0.145 & 0.485 \\\\\n 0.336 & 0.622 \\\\\n\\end{arr... | 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 0.176 & 0.271 \\\\\n 0.272 & 0.039 \\\\\n 0.395 & 0.079 \\\\\n 0.403 & 0.547 \\\\\n 0.4... | 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 0.071 & 0.906 \\\\\n 0.136 & 0.906 \\\\\n 0.269 & 0.15 \\\\\n 0.284 & 0.643 \\\\\n 0.38... | 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 -0.469 & 0.336 \\\\\n -0.392 & 0.258 \\\\\n -0.376 & 0.246 \\\\\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 $6$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.08 & 0.401 \\\\\n 0. & 0. \\\\\n 0.158 & 0.874 \\\\\n 0.566 & 0.115 \\\\\n 0.741 & 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 0.266 & 0.568 \\\\\n 0.313 & 0.116 \\\\\n 0.338 & 0.473 \\\\\n 0.39 & 0.937 \\\\\n 0.46... | 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 0.241 & 0.985 \\\\\n 0.455 & 0.076 \\\\\n 0.481 & 0.104 \\\\\n 0.57 & 0.448 \\\\\n 0.68... | 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 0.258 & 0.249 \\\\\n 0.314 & 0.208 \\\\\n 0.44 & 0.224 \\\\\n 0.516 & 0.87 \\\\\n 0.537... | 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 -0.175 & 0.612 \\\\\n -0.092 & 0.684 \\\\\n 0. & 0. \\\\\n 0.107 & 0.024 \\\\\n 0.349 &... | 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 0.294 & 0.126 \\\\\n 0.436 & 0.504 \\\\\n 0.766 & 0.663 \\\\\n 0.824 & 0.918 \\\\\n 0.8... | 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. & 0. \\\\\n 0.084 & 0.542 \\\\\n 0.098 & 0.014 \\\\\n 0.173 & 0.029 \\\\\n 0.259 & 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 -0.094 & 0.124 \\\\\n 0. & 0. \\\\\n 0.019 & 0.657 \\\\\n 0.05 & 0.714 \\\\\n 0.137 & 0... | 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 -0.249 & 0.645 \\\\\n -0.099 & 0.192 \\\\\n 0. & 0. \\\\\n 0.169 & 0.766 \\\\\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 0.077 & 0.616 \\\\\n 0.144 & 0.217 \\\\\n 0.144 & 0.819 \\\\\n 0.333 & 0.101 \\\\\n\\en... | 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 0.216 & 0.488 \\\\\n 0.326 & 0.068 \\\\\n 0.444 & 0.458 \\\\\n 0.641 & 0.869 \\\\\n 0.8... | 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 0.035 & 0.717 \\\\\n 0.177 & 0.3 \\\\\n 0.178 & 0.707 \\\\\n 0.357 & 0.649 \\\\\n 0.43 ... | 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 -0.081 & 0.191 \\\\\n 0. & 0. \\\\\n 0.326 & 0.002 \\\\\n 0.405 & 0.724 \\\\\n 0.511 & ... | 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 0.022 & 0.842 \\\\\n 0.051 & 0.345 \\\\\n 0.324 & 0.193 \\\\\n 0.434 & 0.916 \\\\\n 0.5... | 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 -0.342 & 0.021 \\\\\n -0.323 & 0.002 \\\\\n -0.284 & 0.342 \\\\\n -0.163 & 0.518 \\\\\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 $\\left(\n\\begin{array}{cc}\n 0.288 & 0.068 \\\\\n 0.323 & 0.591 \\\\\n 0.745 & 0.07 \\\\\n\\end{array}\n\\right)$. E... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n 0.069 & 0.432 \\\\\n 0.835 & 0.1 \\\\\n 0.86 & 0.018 \\\\\n 0.869 & 0.783 \\\\\n\\end{a... | 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 $\\left(\n\\begin{array}{cc}\n 0.403 & 0.48 \\\\\n 0.781 & 0.091 \\\\\n 0.895 & 0.799 \\\\\n\\end{array}\n\\right)$. E... | geometry | polygons |
[
{
"role": "system",
"content": "You are a mathematics tutor. Answer the following math problem."
},
{
"role": "user",
"content": "A polygon with $4$ vertices has the coordinates $\\left(\n\\begin{array}{cc}\n -0.3 & 0.09 \\\\\n 0. & 0. \\\\\n 0.077 & 0.455 \\\\\n 0.501 & 0.163 \\\\\n\\end{array}... | geometry | polygons |
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