Question

If the distance between the points $(5,-2)$ and $(1,a)$ is $5$ units, then the sum of all possible values(s) of $a$ is

• A. $-3$
• B. $1$
• C. $-4$
• D. $4$

Answer 1

The correct option is C $-4$

Distance between two points
$5=\sqrt{(5-1{)}^2+(-2-a{)}^2}$
$\Rightarrow 5=\sqrt{16+4+a^2+4a}\Rightarrow 25=20+a^2+4a\Rightarrow a^2+4a-5=0\Rightarrow (a+5)(a-1)=0\Rightarrow a=-5,1$

Hence, the sum of possible values of $a$ is $-4$.