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.

Answer 1

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