Question 1023728
Some unknown point  (x,y).
{{{sqrt((x-(-7))^2+(y-(-4))^2)=(1/5)sqrt((-7-3)^2+(-4-6)^2)}}}
{{{sqrt((x+7)^2+(y+4)^2)=(1/5)sqrt(100+100)}}}
{{{sqrt((x+7)^2+(y+4)^2)=(1/5)*10*sqrt(2)}}}
{{{sqrt((x+7)^2+(y+4)^2)=2*sqrt(2)}}}
{{{(x+7)^2+(y+4)^2=8}}}


Line AB is  {{{y-6=((6-(-4))/(3-(-7)))(x-3)}}}
{{{y-6=1*(x-3)}}}
{{{y-6=x-3}}}
{{{y=x-3+6}}}
{{{y=x+3}}}
Or some general point   (x, x+3).


The previous, distance formula derived equation then becomes
{{{(x+7)^2+(x+3+4)^2=8}}}

{{{(x+7)^2+(x+7)^2=8}}}

{{{2(x+7)^2=8}}}

{{{(x+7)^2=4}}}

{{{x+7=0+- 2}}}

{{{x=-7+- 2}}}

EITHER x=-9   OR  x=-5.



One of those will work and the other one will not work.
Take {{{highlight(x=-5)}}}.  The corresponding y, being on line AB will be {{{x+3=-5+3=-2}}}; for the point  (-5,-2).