Question 1121605
A point on the y-axis will have x=0.
The point can be the ordered pair  (0,y).


Point (0,y) is same distance from  (5,1) as from (-3,-1).


Using the Distance Formula,
{{{sqrt((0-5)^2+(y-1)^2)=sqrt((0-(-3))^2+(y-(-1))^2)}}}



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


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


{{{16-2y=2y}}}


{{{16=4y}}}


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

The point asked for is  (0,4).