Find the point on x - axis which is equidistant from the following pair of points:

(3, 2) and (- 5, - 2)

Given points are A(3, 2) and B(- 5, - 2).

We need to find a point on x - axis which is equidistant from these points.

Let us assume the point on x - axis be S(x, o).

We know that distance between the points (x₁, y₁) and (x₂, y₂) is .

From the problem,

⇒ SA = SB

⇒ SA² = SB²

⇒ (x - 3)² + (0 - 2)² = (x + 5)² + (0 - (- 2))²

⇒ (x - 3)² + (- 2)² = (x + 5)² + (2)²

⇒ x² - 6x + 9 + 4 = x² + 10x + 25 + 4

⇒ 16x = - 16

⇒ x = - 1

∴ The point on x - axis is (- 1, 0).