Prove that the circumcenter of a triangle is equidistant from its vertices.
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Check the picture below, so, those red ones are the midpoints you found.
![\bf \textit{distance between 2 points}\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) \stackrel{midpoint}{JK}&({{ -1}}\quad ,&{{ 2}})\quad % (c,d) \stackrel{midpoint}{ML}&({{ 2}}\quad ,&{{ -2}}) \end{array} \\\\\\ d = \sqrt{({{ x_2}}-{{ x_1}})^2 + ({{ y_2}}-{{ y_1}})^2}\implies d_2=\sqrt{[2-(-1)]^2+[-2-2]^2} \\\\\\ d_2=\sqrt{(2+1)^2+(-4)^2}\implies d_2=\sqrt{9+16}\implies d_2=5](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bdistance%20between%202%20points%7D%5C%5C%20%5Cquad%20%5C%5C%0A%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%26x_2%26y_2%5C%5C%0A%25%20%20%28a%2Cb%29%0A%5Cstackrel%7Bmidpoint%7D%7BJK%7D%26%28%7B%7B%20-1%7D%7D%5Cquad%20%2C%26%7B%7B%202%7D%7D%29%5Cquad%20%0A%25%20%20%28c%2Cd%29%0A%5Cstackrel%7Bmidpoint%7D%7BML%7D%26%28%7B%7B%202%7D%7D%5Cquad%20%2C%26%7B%7B%20-2%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0Ad%20%3D%20%5Csqrt%7B%28%7B%7B%20x_2%7D%7D-%7B%7B%20x_1%7D%7D%29%5E2%20%2B%20%28%7B%7B%20y_2%7D%7D-%7B%7B%20y_1%7D%7D%29%5E2%7D%5Cimplies%20d_2%3D%5Csqrt%7B%5B2-%28-1%29%5D%5E2%2B%5B-2-2%5D%5E2%7D%0A%5C%5C%5C%5C%5C%5C%0Ad_2%3D%5Csqrt%7B%282%2B1%29%5E2%2B%28-4%29%5E2%7D%5Cimplies%20d_2%3D%5Csqrt%7B9%2B16%7D%5Cimplies%20d_2%3D5)
now, that many units are each distance for those "medians", hmmm now, recall that each unit is meant to be 10 meters, so, just multiply each by 10, to get how many meters long each one is.
now, that many units are each distance for those "medians", hmmm now, recall that each unit is meant to be 10 meters, so, just multiply each by 10, to get how many meters long each one is.
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