Question

If the distance between the points $(5,-2)$ and $(1,a)$ is $5$ units, then the value of $a$ can be

• A. $1$
• B. $-1$
• C. $5$
• D. $-5$

Answer 1

Answer: (A), (D)

The correct options are
A $1$
D $-5$

$5=\sqrt{(1-5{)}^2+(a-(-2){)}^2}$
$\Rightarrow 5=\sqrt{16+(a+2{)}^2}$
On squaring both sides
$25=16+(a+2{)}^2$
$\Rightarrow (a+2{)}^2=9$
$\Rightarrow (a+2)=\pm 3$
$\Rightarrow a=-5,1$