Find a point on the y axis that is equidistant from (1, 1) and (5, 5).
Would the answer be (-4,-4)
point is (x,0)
(distance to first point)^2 = (x-1)^2 +1^1
(distance to point two)^2 (x-5)^2 + 5^2
so
x^2 -2x+1 + 1 = x^2 -10 x +25 + 25
-2x+2 = -10 x + 50
12 x = 48
x = 4
so
(4,0)