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Question

The points (0,0) and (4,4) are the extremities of a diagonal of a parallelogram. If the third vertex is (4,0). Find the coordinates of the fourth vertex.

A
(0,4)
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B
(3,1)
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C
(2,4)
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D
None of these
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Solution

The correct option is A (0,4)
Given A(0,0),B(4,0),C(4,4) Let the fourth coordinate is P(x,y).

Since the opposite sides of a parallelogram are equal.
So, AB=PC and BC=PA.

So by distance formula we have,

Distance between two points = (x2x1)2+(y2y1)2


Hence 4=(4x)2+(4y)2............(1)

and 4=(x)2+(y)2.........(2)

Solving (1) and (2):

x+y=4.........(3).

So point P lies on this line at a distance 4 units from C and A.
Hence, the required point is P(0,4).




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