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Question
If the points A(2, 3), B(–5, 6), C(6, 7) and D(p, 4) are the vertices of a parallelogram ABCD, find the value of p.
Solution
Given that,
`\implies` A(2, 3), B(–5, 6), C(6, 7) and D(p, 4)
We know that, diagonals of a parallelogram bisect each other
So, midpoint of line segment joining points A and C is same as midpoint of line segment joining points B and D
`\implies [(2 + 6)/7, (3 + 7)/2] = [(-5 + "p")/2, (6 + 4)/2]`
`\implies` (4, 5) = `[("p" - 5)/2, 5]`
On comparing,
`\implies ("p" - 5)/2` = 4
`\implies` p – 5 = 8
`\implies` p = 13
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