Question

Find the value of a when the distance between the points (3,a) and (4,1) is $\sqrt{10}$.

Answer 1

$D=\sqrt{(4-3{)}^2+(1-a{)}^2}=\sqrt{10}$

$D=\sqrt{(1+1+a^2-2a)}=\sqrt{10}$
=$\sqrt{(2+a^2-2a)}=\sqrt{10}$
$\Rightarrow a^2-2a+2-10=0$
$\Rightarrow a^2-2a-8=0$
$\Rightarrow a^2-4a+2a-8=0$
$\Rightarrow a(a-4)+2(a-4)=0$
$\Rightarrow (a+2)(a-4)=0$
$\Rightarrow a=4,-2$