If (1, 2), (4, 6), (x, 6)and (3, 2)are the vertices of a parallelogram taken in order, then the value of x is

Here we have the parallelogram with vertices

(1, 2), (4, 6), (x, 6)and (3, 2).

Let the vertices be A(1,2),B(4,6),C(x,6) and D(3,2)

Since the vertices are taken in order AC and BD are the diagonals of the parallelogram.

In a parallelogram diagonals bisect each other.

∴Mid–point of AC = Mid–point of BD

Mid–point of two points (x₁,y₁) and (x₂,y₂) is

Here Mid–point of AC = –––(1)

Mid–point of BD = –––(2)

(1) = (2)

⇒

Now we will equate the corresponding coordinates.

∴

⇒ 2(1 + x) = 7×2

⇒ 2 + 2x = 14

⇒ 2x = 12

⇒ x = 6