Question

If $C$ is the reflection of $A\left(2,4\right)$ in $X‐axis$ and $B$ is the reflection of $C$ is $Y-axis$, then $\left|AB\right|$ is equal to

• 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 options:

Finding the value of $AB$:

Given that $C$ is the reflection of $A\left(2,4\right)$ in $X‐axis$ and $B$ is the reflection of $C$ is $Y‐axis$.

Hence, the coordinates are $A\left(2,4\right),B\left(-2,-4\right)$ and $C\left(2,-4\right)$

$\therefore \left|AB\right|=\sqrt{\left[{\left(-2-2\right)}^2+{\left(-4-4\right)}^2\right]}$

⇒ $\left|AB\right|=\sqrt{\left(16+64\right)}$

⇒ $\left|AB\right|=\sqrt{80}$

⇒ $\left|AB\right|=4\sqrt{5}$

Hence, option (C) is correct.