Question

Find the point on the y-axis that is equidistant from (5 ,1) and (-3 -1). The answer is (0,4) but I don't know the process.

Answer 1

any point equidistant from the two given points must lie on the right bisector of the line joining the two points, so ...

midpoint of given points is (1,0)
slope of line joining the given points
= (-1-1)/(-3-5) = 1/4
so the slope of the right-bisector must be -4

equation of right-bisector:
y = -4x + b, but (1,0) lies on it, then
0 = -4 + b
b = 4

equation of right-bisector: y = 4x + 4

of course the y-intercept of y = mx+b is b
so the y-intercept is 4
or the point (0,4)