Question

A point $P(2,-1)$ is equidistant from points $(a,7)$ and $(-3,a)$. Find $a$.

Answer 1

$\sqrt{(2-(-3){)}^2+(-1-a{)}^2}=\sqrt{(2-a{)}^2+(-1-7{)}^2}$

Squaring both sides

$(2+3{)}^2+(1+a{)}^2=(2-a{)}^2+(-8{)}^2$

$\Rightarrow 25+1+a^2+2a=4+a^2-4a+64$

$\Rightarrow 6a=42$

$\Rightarrow a=7$.