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Question

The fourth vertex D of a parallelogram ABCD whose three vertices are A(2,3),B(6,7) and C(8,3) is

A
(0,1)
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B
(0,1)
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C
(4,1)
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D
(1,4)
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Solution

The correct option is C (4,1)
Let A(2,3),B(6,7) and C(8,3) be the vertices of parallelogra

And let D(x,y) be the fourth vertex.

Midpoint of AC =(2+82,3+32)=(5,3)

Also, midpoint of BD =(x+62,y+72)

Since the diagonals of parallelogram bisect eachother at O

Therefore, midpoint of AC = midpoint of BD

(x+62,y+72)=(5,3)
x+62=5,y+72=3

x+6=10,y+7=6

x=4,y=1

Therefore, the coordinates of the fourth vertex will be (x,y)=(4,1).

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