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Question
A(–1, 0), B(1, 3) and D(3, 5) are the vertices of a parallelogram ABCD. Find the co-ordinates of vertex C.
Solution
Let the co-ordinates of vertex C be (x, y).
ABCD is a parallelogram.
∴ Mid-point of AC = Mid-point of BD
`((-1 + x)/2, (0 + y)/2) = ((1 + 3)/2, (3 + 5)/2)`
`((-1 + x)/2, y/2) = (2,4)`
`(-1 + x)/2 = 2 and y/2 = 4`
`x = 5` and `y/2 = 4`
x = 5 and y = 8
Thus, the co-ordinates of vertex C is (5, 8).
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