Question

find x so that the distance between (-2,3) and (x,1) is square root 13

Answer 1

EXPLANATION.

Distance between (-2,3) and (x,1) is √13.

As we know that,

Distance Formula.

⇒ d = √(x₂ - x₁)² + (y₂ - y₁)².

Using this formula in the equation, we get.

⇒ √13 = √(x + 2)² + (1 - 3)².

⇒ √13 = √(x + 2)² + (- 2)².

⇒ 13 = (x + 2)² + 4.

⇒ 13 - 4 = (x + 2)².

⇒ 9 = (x + 2)².

⇒ x² + 4 + 4x = 9.

⇒ x² + 4x + 4 - 9 = 0.

⇒ x² + 4x - 5 = 0.

Factorizes the equation into middle term splits, we get.

⇒ x² + 5x - x - 5 = 0.

⇒ x(x + 5) - 1(x + 5) = 0.

⇒ (x - 1)(x + 5) = 0.

⇒ x = 1  and x = - 5.