Question

If $C$ is the reflection of $A(2,4)$ in $x$-axis and $B$ is the reflection of $C$ in $y$-axis, then $\left|AB\right|$ is

• A. $20$
• B. $2\sqrt{5}$
• C. $4\sqrt{5}$
• D. $4$

Answer 1

Answer: (C)

$4\sqrt{5}$

Here, coordinates are $A(2,4),B(-2,-4)$ and $C(2,-4)$.
Now, $\left|AB\right|=\sqrt{{(-2-2)}^2+{(-4-4)}^2}$
$=\sqrt{16+64}=\sqrt{80}$
$=4\sqrt{5}$