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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)
the coordinate of the fourth vertex D.

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Solution

The coordinate of fourth point be (x,y).
Given three coordinates of parallelogram-
A(3,6)
B(5,10)
C(3,2)

Now,
Mid-point of AC will be equal to mid-point of BD.
Therefore,
Mid-point of AC=(3+32,6+22)=(3,4)

Mid-point of BD=(x+52,y+102)

Now,
x+52=3x=1
y+102=4y=2
Hence the coordinate of fourth point will be (1,2).

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