Given points are A(7, 6) and B(- 3, 4).
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 - 7)2 + (0 - 6)2 = (x - (- 3))2 + (0 - 4)2
⇒ (x - 7)2 + (- 6)2 = (x + 3)2 + (- 4)2
⇒ x2 - 14x + 49 + 36 = x2 + 6x + 9 + 16
⇒ 20x = 60
⇒ x = 60/20
⇒ x = 3
∴ The point on x - axis is (3, 0).
