The three vertices of a parallelogram ABCD, taken in order, are A(-1, 0), B(3, 1) and C(2, 2). Find the co-ordinates of the fourth vertex of the parallelogram.
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Question

The three vertices of a parallelogram ABCD, taken in order, are A(-1, 0), B(3, 1) and C(2, 2). Find the co-ordinates of the fourth vertex of the parallelogram.

KnowledgeBoat · Accepted Answer

Let coordinates of D be (x, y). By using mid-point formula, (x, y) = Mid-point of AC : Midpoint of Diagonal BD : Since its a parallelogram, the midpoint of diagonal AC must be equal to the midpoint of diagonal BD, as diagonals bisect each other. Equating the x-coordinates: ⇒ 3 + x = 1 ⇒ x = 1 - 3 ⇒ x = -2. Equating the y-coordinates: ⇒ 1 + y = 2 ⇒ y = 2 - 1 ⇒ y = 1. Hence, coordinates of D = (-2, 1).

Mathematics

The three vertices of a parallelogram ABCD, taken in order, are A(-1, 0), B(3, 1) and C(2, 2). Find the co-ordinates of the fourth vertex of the parallelogram.

Section Formula

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