Given points are A(6, 5) and B(- 4, 3).
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 - 6)2 + (y - 5)2 = (0 - (- 4))2 + (y - 3)2
⇒ (- 6)2 + (y - 5)2 = (4)2 + (y - 3)2
⇒ 36 + y2 - 10y + 25 = 16 + y2 - 6y + 9
⇒ 4y = 36
⇒ y = 36/4
⇒ y = 9
∴ The point on y - axis is (0, 9).
