Question 963246
Use the distance formula from a point on the line (x,y) to each point. 
Since the distances are equal, set them equal to each other.
{{{(x-3)^2+(y+2)^2=(x+3)^2+(y-4)^2}}}
{{{x^2-6x+9+y^2+4y+4=x^2+6x+9+y^2-8y+16}}}
{{{-6x+4y+13=6x-8y+25}}}
{{{12y=12x+12}}}
{{{y=x+1}}}