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If $\mathrm{C}$ is the reflecton of $\mathrm{A}(2,4)$ in $\mathrm{x}$-axis and $\mathrm{B}$ is the reflection of $\mathrm{C}$ in $\mathrm{y}$-axis, then $|\mathrm{AB}|$ is
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The correct answer is:
$4 \sqrt{5}$
$$
\begin{aligned}
& \text { Hints: } \mathrm{A} \equiv(2,4) ; \mathrm{C} \equiv(2,-4) ; \mathrm{B} \equiv(-2,-4) \\
& |A B|=\sqrt{(2-(-2))^2+(4-(-4))^2}=\sqrt{4^2+8^2} \\
& =\sqrt{16+64}=\sqrt{80}=\sqrt{16 \times 5}=4 \sqrt{5}
\end{aligned}
$$
\begin{aligned}
& \text { Hints: } \mathrm{A} \equiv(2,4) ; \mathrm{C} \equiv(2,-4) ; \mathrm{B} \equiv(-2,-4) \\
& |A B|=\sqrt{(2-(-2))^2+(4-(-4))^2}=\sqrt{4^2+8^2} \\
& =\sqrt{16+64}=\sqrt{80}=\sqrt{16 \times 5}=4 \sqrt{5}
\end{aligned}
$$
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