Question

The point on the y-axis which is equidistant from the points \( (5, -2) \) and \( (-3, 2) \) is:

• A. \( (0, 3) \)
• B. \( (-2, 0) \)
• C. \( (0, -2) \)
• D. \( (2, 2) \)

Hint:

To solve for an unknown point equidistant from two other points, equate the distances from that point to each of the two known points.

Answer 1

The Correct Option is A

Let the required point be \( (0, y) \) on the y-axis.
The distances from \( (0, y) \) to \( (5, -2) \) and \( (0, y) \) to \( (-3, 2) \) should be equal.
Using the distance formula for each point, we have two equations: \[ \sqrt{(5 - 0)^2 + (-2 - y)^2} = \sqrt{(-3 - 0)^2 + (2 - y)^2} \]
Squaring both sides and solving for \( y \), we get \( y = 3 \).
Therefore, the point is \( (0, 3) \).