Find the coordinates of the intersection of the diagonals of parallelogram WXYZ with the following vertices: W (-1, 7), X (8, 7), Y (6, -2) and Z (-3, -2)

Respuesta :

check the picture below

in a parallelogra, the diagonals "bisect" each other, thus each one cuts the other in 2 equal halves.

that simply means in this case, where they intersect, is the midpoint of either diagonal... so let's use the midpoint of XZ then

[tex]\bf \textit{middle point of 2 points }\\ \quad \\ \begin{array}{lllll} &x_1&y_1&x_2&y_2\\ % (a,b) X&({{ 8}}\quad ,&{{ 7}})\quad % (c,d) Z&({{ -3}}\quad ,&{{ -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{{{ -3}} + {{ 8}}}{2}\quad ,\quad \cfrac{{{ -2}} + {{ 7}}}{2} \right)[/tex]
Ver imagen jdoe0001