Question

If points $(3,K)$ and $(K,5)$ are equidistant from a point $(0,2)$, then find the value of $K$.

Answer 1

$d=\left[\right(3-0{)}^2+(k-2{)}^2{]}^{1/2}$ ……..$\left(1\right)$

$d=\left[\right(k-0{)}^2+(5-2{)}^2{]}^{1/2}$ ………..$\left(2\right)$

$\left(1\right)=\left(2\right)$

Squaring both sides

$3^2+(k-2{)}^2=k^2+3^2$

Take square root both sides

$k-2=\pm k$

$(+)$ $k-2=k$

$k-2=0$ not possible

$(-)$ $k-2=-k$

$k=1$.