Question

The point on \( y \)-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:

For points on the y-axis, their x-coordinate is always 0. Solve using the distance formula and equate both distances.

Answer 1

The Correct Option is C

Let the required point on the y-axis be \( (0, y) \).
Since it is equidistant from \( (5, -2) \) and \( (-3,2) \), we use the distance formula:
\[ \sqrt{(0 - 5)^2 + (y + 2)^2} = \sqrt{(0 + 3)^2 + (y - 2)^2} \] Squaring both sides:
\[ (5)^2 + (y+2)^2 = (3)^2 + (y-2)^2 \] \[ 25 + y^2 + 4y + 4 = 9 + y^2 - 4y + 4 \] Cancel \( y^2 \) and simplify:
\[ 25 + 4y + 4 = 9 - 4y + 4 \] \[ 29 + 4y = 13 - 4y \] \[ 8y = -16 \] \[ y = -2 \] So the point is \( (0,-2) \).