Question 1203326
On the y-axis, some point (0,y).
That point equally distant from (5,1) and (-3, -1);
Use the distance formula.


{{{sqrt((5-0)^2+(1-y)^2)=sqrt((-3-0)^2+(-1-y)^2)}}}
Simplify and solve this.


{{{25+(1-y)^2=9+(-1-y)^2}}}

{{{16=(-1-y)^2-(1-y)^2}}}

{{{16=1+2y+y^2-(1-2y+y^2)}}}

{{{16=4y}}}

{{{highlight(y=4)}}}