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 = -16/16
⇒ x = - 1
∴ The point on x - axis is (- 1, 0).