Question

The coordinates of triangle ABC areA(0,0), B(2,6), and C(4,2). Using coordinates geometry; prove that, if the midpoints of sides AB and AC are joined, the segment formed is parallel to the third side and equal to one- half the length of the third side.

Answer 1

Hint:
Parallel means they have the same slope.

Slope BC = (yc-yb)/(xc-xb)=-2
Let H be mid-point of AB = (1,3)
Let K be mid-point of AC = (2,1)
Slope of HK = (yk-yh)/(xk-xh)=-2/1=-2
Therefore HK is parallel to BC.