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in Coordinate Geometry by (44.5k points)
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If (6,8), (3,7) and (-2,-2) be the coordinates of the three consecutive vertices of a parallelogram, find coordinates of the fourth vertex.

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Let the coordinates of the fourth vertex D be (x, y).

We know that diagonals of a parallelogram bisect each other.

∴ Midpoint of AC = Midpoint of BD …(i)

Coordinates of the midpoint of AC are

⇒ 3 + x = 4 and 7 + y = 6

⇒ x = 1 and y = -1

Thus, the coordinates of the vertex D are (1, -1)

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