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Question

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

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Solution

Let the co-ordinates of vertex C be (x,y).
ABCD is a parallelogram.
Mid-point of AC= Mid-point of BD.
(1+x2,0+y2)=(1+32,3+52)

(1+x2,y2)=(2,4)

1+x2=2 and y2=4

1+x=4 and y2=4

x=5 and y=8
The co-ordinates of vertex C is (5,8).

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