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Question
Three vertices of a parallelogram taken in order are (−1, −6), (2, −5) and (7, 2). The fourth vertex is
Options
(1, 4)
(4, 1)
(1, 1)
(4, 4)
(0, 0)
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Solution
(4,1)
Let A(−1, −6), B(2, −5) and C(7, 2) be the given vertex. Let D(h, k) be the fourth vertex.
The midpoints of AC and BD are \[\left( 3, - 2 \right) \text { and } \left( \frac{2 + h}{2}, \frac{- 5 + k}{2} \right)\] respectively.
We know that the diagonals of a parallelogram bisect each other.
\[\therefore 3 = \frac{2 + h}{2} and - 2 = \frac{- 5 + k}{2}\]
\[ \Rightarrow h = 4 \text { and } k = 1\]
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