Question

If distance between the points (5,3) and $(x,-1)$ are 5 unit, then find the value of $x$.

Answer 1

Let distance between points $A(5,3)$ and $B(x,-1)$ is 5 unit, then
According to question $5=\sqrt{(5-x{)}^2+[3-(-1){]}^2}$
Squaring both sides

$\Rightarrow 25=(5-x{)}^2+(3+1{)}^2$
$\Rightarrow 25=(5-x{)}^2+16$
$\Rightarrow 25=25+x^2-10x+16$
$\Rightarrow x^2-10x+16=0$
$\Rightarrow x^2-8x-2x+16=0$
$\Rightarrow x(x-8)-2(x-8)=0$
$\Rightarrow (x-2)(x-8)=0$
if $x-8=0\Rightarrow x=8$
and $x-2=0\Rightarrow x=2$
Hence value of $x$ are $8$ and $2$