Q15 of 77 Page 7


Three consecutive vertices of a parallelogram are (-2, -1), (1, 0) and (4, 3).Find the fourth vertex.

(1,2)
SOLUTION:

Let A(-2, -1), B(1, 0), C(4, 3) and D(x, y) be the vertices of a parallelogram ABCD. Since, the diagonals of a parallelogram bisect each other.
Therefore coordinates of the mid-point of AC = Coordinates of the mid-point of BD.

We know that the midpoint of a line segment AB with A(x, y) and B(u, v) is ⇒ 1 + x = 2, y = 2
⇒ x = 1, y = 2
Therefore (1, 2) is the fourth vertex.

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