Question

If the distance between the two points $P(a,3)$ and $Q(4,6)$ is $5$, then find $a$.

• A. $0$
• B. $-4$
• C. $8$
• D. $-4$ and $0$
• E. $0$ and $8$

Answer 1

The correct option is E $0$ and $8$

The distance between points $(a,3)$ and $(4,6)$ is $\sqrt{{(a-4)}^2+{(3-6)}^2}=\sqrt{{(a-4)}^2+9}$
Given that the distance is $5$
So, we have $\sqrt{{(a-4)}^2+9}=5$ $\Rightarrow {(a-4)}^2+9=25$
$\therefore a-4=\sqrt{16}=|4|$
So, we get $a=4+|4|=0,8$