geometry
posted by Sindy .
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.

Hint:
Parallel means they have the same slope.
Slope BC = (ycyb)/(xcxb)=2
Let H be midpoint of AB = (1,3)
Let K be midpoint of AC = (2,1)
Slope of HK = (ykyh)/(xkxh)=2/1=2
Therefore HK is parallel to BC.