Question

If the points A (6, 2), B (2, k), С (1, 5), and D (5, 6), taken in order, are the vertices of a parallelogram, find the value of k.

Answer 1

Here, using the parallelogram property that the diagonals bisect each other,

So, A + C = B + D (vector/midpoint equality),

⇒ A + C = (6 + 1, 2 + 5)

= (7, 7)

⇒ B + D = (2 + 5, k + 6)

= (7, k + 6)

k + 6 = 7

k = 7 − 6

∴ k = 1

Hence, the value of k is 1.