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Mid Point

A -1,0, B1,3 ...

Question

A (-1,0), B(1,3) and D(3,5) are the vertices of a parallelogram ABCD.Find the co-ordinates of vertex C.

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Solution

Let the co-ordinates of the fourth vertex C be (x, y).We know that diagonals of a parallelogram bisect each other.Mid-point of BD = Mid-point of ACCoordinates of the mid-point of BD are

Coordinates of the mid-point of AC are

$fraction numerator x minus 1 over denominator 2 end fraction equals space 2 space rightwards double arrow space x minus 1 equals 4 space rightwards double arrow space x equals 5 y over 2 equals 4 space rightwards double arrow space y equals 8$
Thus, the co-ordinates of the vertex C are (5, 8).

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