Question

A right triangle has vertices P(-2,5), Q(5,2) and R(8,9). Whatare the coordinates of the midpoint of the hypotenuse?

Answer 1

Answer:

D. (3, 7)

Explanation:

First, we need to draw the triangle to identify the hypotenuse, so using the points P(-2, 5), Q(5, 2), and R(8, 9), we get:

Therefore, the hypotenuse is side PR.

Then, the midpoint of a segment that goes from (x1, y1) to (x2, y2) is

$(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

So, replacing (x1, y1) = P(-2, 5) and (x2, y2) = R(8, 9), we get that the midpoint of the hypotenuse is

$(\frac{-2+8}{2},\frac{5+9}{2})=(\frac{6}{2},\frac{14}{2})=(3,7)$

Therefore, the answer is D. (3, 7)