Given points are A(- 5, - 2) and B(3, 2).
We need to find a point on y - axis which is equidistant from these points.
Let us assume the point on y - axis be S(0, y).
We know that distance between the points (x1, y1) and (x2, y2) is
From the problem,
⇒ SA = SB
⇒ SA2 = SB2
⇒ (0 - (- 5))2 + (y - (- 2))2 = (0 - 3)2 + (y - 2)2
⇒ (5)2 + (y + 2)2 = (- 3)2 + (y - 2)2
⇒ 25 + y2 + 4y + 4 = 9 + y2 - 4y + 4
⇒ 8y = - 16
⇒ y = -16/8
⇒ y = - 2
∴ The point on y - axis is (0, - 2).