Question

Find $a$ if the distance between the points $P(11,-2)$ and $Q(a,1)$ is $5$ units.

Answer 1

$PQ=5$

$\sqrt{(a-11{)}^2+(1+2{)}^2}=5$

$(a-11{)}^2=16$

$a-11=\sqrt{16}$

$a-11=\pm 4$

$a=15$ or $7$.