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 = -56/8
⇒ x = - 7
∴ The point on x - axis is (- 7, 0).
