Question

If $(2,-4)$ is equidistant from $(3,8)$ and $(-10,y)$. find the value of $y$.

Answer 1

$\sqrt{(2-3{)}^2+(-4-8{)}^2}=\sqrt{\{2-(-10){\}}^2+(-4-y{)}^2}$

$\sqrt{1-144}=\sqrt{144+(4+y{)}^2}$

$\therefore (y+4{)}^2=1$

$y+4=+1$ $y+4=-1$

$y=-3$ $y=-5$.