The fourth vertex D of a parallelogram ABCD whose three vertices are A( - 2, 3), B(6, 7) and C(8, 3) is


Given a parallelogram ABCD whose three vertices are;

A ( - 2, 3),


B (6, 7) and


C (8, 3)



Let the fourth vertex of parallelogram, D = (x4, y4) and L, M be the middle points of AC and BD, respectively


L =


Since, mid - point of a line segment having points (x1, y1) and (x2, y2)


= and


M =


As we know ABCD is a parallelogram, therefore diagonals AC and BD will bisect each other.


So, L and M are the same points


3 = and


3 =


6 = 6 + x4 and 6 = 7 + y4


x4 = 0 and y4 = 6 – 7


x4 = 0 and y4 = - 1


Hence, the fourth vertex of parallelogram is D = (x4, y4) = (0, 1)

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