Question

If the vertices of a square are A(–2, 4), B(4, 4), C(4, –2), and D(–2, –2), what are the coordinates of the point where the diagonals intersect?

Answer 1

Check the picture below.

notice, is just a 6x6 square, therefore its diagonals will cut each other in half, thus they both will meet at their midpoint, so let's check the midpoint for AC then,

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points }\\ \quad \\ \begin{array}{ccccccccc} &&x_1&&y_1&&x_2&&y_2\\ % (a,b) &A&(~{{ -2}} &,&{{ 4}}~) % (c,d) &C&(~{{ 4}} &,&{{ -2}}~) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left( \cfrac{4-2}{2}~~,~~\cfrac{-2+4}{2} \right)\implies \left( \cfrac{2}{2}~~,~~\cfrac{2}{2} \right)\implies (1,1)$