Question

If the distance between two points $(x,7)$ and $(1,15)$ is $10,$ find the value of $x$.

Answer 1

Using distance formula, we have

$\sqrt{(x-1{)}^2+(7-15{)}^2}=10$

$\Rightarrow (x-1{)}^2+8^2={10}^2$ [Squaring both sides]

$\Rightarrow (x-1{)}^2=100-64$

$\Rightarrow (x-1{)}^2=6^2$

$\Rightarrow (x-1{)}^2=\pm 6$

if $(x-1)=6$

then $x=7$

and, if $(x-1)=-6$

then $x=-5$