midpoint

Question

0

45

1

+789

In triangle $PQR,$ $M$ is the midpoint of $\overline{QR}.$ Find $PM.$
PQ = 5, PR = 8, QR = 11

bingboy Nov 29, 2023

bader · Answer 1 · 2023-11-29T04:46:47

By the Pythagorean Theorem, PQ2+PR2=QR2, so 52+82=112.

Thus △PQR is a right triangle where PQ is the hypotenuse, so by the Pythagorean Theorem, PM2=(2PR)2=(28)2=16.

Hence, PM=16=4.