Question

A (5, 3), B (-1, 1) and C (7, -3) are the vertices of triangle ABC. If L is the mid-point of AB and M is the mid-point of AC, show that : LM=$\frac{1}{2}$ BC.

Answer 1

L = [ (5-1)/2, (3+1)/2 ] = (2, 2) formula for midpoint: [ (x1+x2)/2 , (y1+y2)/2 ]
M = [ (5+7)/2, (3-3)/2 ] = (6, 0)

LM² = (6-2)² + (0-2)² = 20 => LM = 2√5 as distance² = (x1-x2)²+(y1-y2)²

BC² = (7+1)² + (-3-1)² = 80 => BC = 4√5

Hence LM = BC/2