What are the coordinates of these two points?

Question

The point (5,-3) is a distance of 13 units from two points located on the y-axis.

Answer 1

Any point on the y-axis can be expressed as (0,y).

So, the distance from (5,-3) to (0,y) is 13.

√[(0-5)² + (y+3)²] = 13

y² + 6y + 34 = 169

y² + 6y - 135 = 0

(y + 15)(y - 9) = 0

y = 9 or y = -15

The points are (0,9) and (0,-15)