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Question
The three vertices of a parallelogram taken in order are (-1, 0), (3, 1) and (2, 2) respectively. Find the coordinates of the fourth vertex.
Solution
Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order.
Since, the diagonals of a parallelogram bisect each other.
So, coordinates of the mid point of AC = coordinates of mid point of BD
⇒ `((-1 + 2)/2,(0 + 2)/2) = ((3 + x)/2 ,(y + 1)/2)`
⇒ `(1/2,1) = ((3 + x)/2 ,(y + 1)/2)`
`(3 + x)/(2) = (1)/(2)`
⇒ x = -2
Also `(y + 1)/(2)` = 1
⇒ y + 1 = 2
⇒ y = 1
The forth vertex of parallelogram = (-2, 1).
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