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

(2, - 5) and (- 2, 9)

Given points are A(2, - 5) and B(- 2, 9).

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 - 2)² + (0 - (- 5))² = (x - (- 2))² + (0 - 9)²

⇒ (x - 2)² + (5)² = (x + 2)² + (- 9)²

⇒ x² - 4x + 4 + 25 = x² + 4x + 4 + 81

⇒ 8x = - 56

⇒ x = - 7

∴ The point on x - axis is (- 7, 0).