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Question

Three vertices of a parallelogram ABCD taken in order are A(3, 6), B (5, 10) and C(3, 2). Then the coordinates of the fourth vertex D is


A

(1, -2)

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B

(-1, 2)

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C

(2, -1)

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D

(-2, 1)

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Solution

The correct option is A

(1, -2)


Let the coordinates of the vertex D be (x, y)
Mid-point of AC = Mid -point of BD
[ Diagonals of a parallelogram bisect each other]

We know that mid-point of the line joining two points A(x1,y1) and B(x2,y2) is given by (x1+x22,y1+y22)
(3+32,6+22)=(x+52,y+102)(62,82)=(x+52,y+102)(3,4)=(x+52,y+102)x+52=3 and y+102=4x+5=6 and y+10=8x=1 and y=2
Coordinates of the fourth vertex D are (1, -2)


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