If A(1, 3), B(-1, 2), C(2, 5) and D(x, 4) are the vertices of a llgm ABCD then the value of x is

Question

Philoid · Accepted Answer

Since the given quadrilateral is a parallelogram, the length of parallel sides is equal.

So by distance formula,

⇒ Distance AB =

= √(4 + 1)

= √5

⇒ Distance CD =

=

⇒ Distance CD = Distance AB

⇒ =

Squaring both sides

⇒ 5 = (x-2)² + 1

⇒ 4 = (x-2)²

Taking square root of both sides

⇒ 2 = x-2

⇒ x = 4

or

⇒ -2 = x-2

⇒ x = 0

Therefore the value of x can be 0 or 4.