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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.

  • geometry -

    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.

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