How would I find a point on the y-axis equidistant from two other points? The points are$$(5,-5) and (1,1)$$
I tried doing this visually and came up with (0,-5). This wasn't correct once I applied the distance formula to check the distance between that point and the two others. 

A point on the $y-$axis is of the form $(0,y)$.
The distance between $(0,y)$ and $(5,-5)$ is:
$$\sqrt{(5-0)^2+(-5-y)^2}=\sqrt{25+(5+y)^2}$$
The distance between $(0,y)$ and $(1,1)$ is:
$$\sqrt{(1-0)^2+(1-y)^2}=\sqrt{1+(1-y)^2}$$
The two distances are equal, so also their squares:
$$25+(5+y)^2=1+(1-y)^2$$
Now you have to solve for $y$.
