Question

In triangle ABC, M is the midpoint of AB. Prove that
MC
is perpendicular to
AB
if A(4, 2), B(0, 4), and C(8, 15)

Answer 1

Step-by-step explanation:

M is the midpoint of AB.  First, find the coordinates of M.

M = ((4 + 0) / 2, (2 + 4) / 2)

M = (2, 3)

Now find the slope of MC:

m = (15 − 3) / (8 − 2)

m = 12 / 6

m = 2

Find the slope of AB:

m = (4 − 2) / (0 − 4)

m = 2 / -4

m = -1/2

The slopes are opposite inverses, so the two are indeed perpendicular.

Answer 2

Answer:

The slope of Ab= -1/2

The slope of MC is 2

Step-by-step explanation:

ab=4-2/0-4

mc=15-3/8-2