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Question

If A(−2,2),B(8,2) and C(4,−4) are the vertices of a parallelogram ABCD. Find the coordinates of the fourth vertex D are:

A
(8,4)
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B
(6,2)
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C
(8,2)
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D
(6,4)
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Solution

The correct option is D (6,4)
Let the vertex of D be x and y.
As we know that the diagonals of parallelogram intersect each other at point O.
So, it is mid-point of the line AC abd BD
Along with AC:
Ox=2+42=1, Oy=2+(4)2=1

Now, along with BD,
Ox=8+x2, Oy=2+y2
Now,
1=8+x2 and 1=2+y2

x=6 and y=4
Co-ordinates of D is (6,4)


1257529_185680_ans_d7182d5ddc484297b06b1f211789ca40.jpeg

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