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Question
Three vertices of a parallelogram, taken in order, are (−1, −6), (2, −5) and (7, 2). Write the coordinates of its fourth vertex.
Solution
Let \[A\left( - 1, - 6 \right), B\left( 2, - 5 \right)\text{ and }C\left( 7, 2 \right)\] be the vertices of the parallelogram ABCD.
Let the coordinates of D be (x, y).
Since, diagonals of a parallelogram bisect each other,
\[\frac{- 1 + 7}{2} = \frac{2 + x}{2}\text{ and }\frac{- 6 + 2}{2} = \frac{- 5 + y}{2}\]
\[ \Rightarrow x = 4\text{ and }y = 1\]"
Hence, the coordinates of the fourth vertex D are (4, 1).
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