Question

A parallelogram has vertices E(1, 4), F(5, 3), G(−3, 1), and H(1, 0). What are the coordinates of the midpoint of each diagonal?

Answer 1

Check the picture below.

now, the diagonals cut each other in two equal halves, thus, the midpoint of GF is the same coordinates as the midpoint for EH, so let's check what the midpoint for GF is then

$\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) G&({{ -3}}\quad ,&{{ 1}})\quad % (c,d) F&({{ 5}}\quad ,&{{ 3}}) \end{array}\qquad % coordinates of midpoint \left(\cfrac{{{ x_2}} + {{ x_1}}}{2}\quad ,\quad \cfrac{{{ y_2}} + {{ y_1}}}{2} \right) \\\\\\ \left(\cfrac{5-3}{2}~~,~~\cfrac{5-1}{2} \right)\implies \left( \cfrac{2}{2}~~,~~\cfrac{4}{2} \right)\implies (1,2)$