Question

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

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

Answer 1

The correct option is C

$4\sqrt{5}$

Explanation for the correct option:

Find the value of $\left|AB\right|$:

Given, $A=(2,4)$

From the figure we can see

$C=(2,-4)$ and $B=(-2,-4)$

By using distance formula, we get

$\begin{array}{rcl}\therefore AB& =& \sqrt{\left[{(-2-2)}^2+{(-4-4)}^2\right]}\\ & =& \sqrt{(16+64)}\\ & =& \sqrt{80}\\ & =& \mathbf{4}\sqrt{\mathbf{5}}\end{array}$

Hence, option ‘C’ is correct.