WBJEE · Maths · Straight Lines
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
- A 20
- B \(2 \sqrt{5}\)
- C \(4 \sqrt{5}\)
- D 4
Answer & Solution
Correct Answer
(C) \(4 \sqrt{5}\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} & \text { Hints: } \mathrm{A} \equiv(2,4) ; \mathrm{C} \equiv(2,-4) ; \mathrm{B} \equiv(-2,-4) \\ & |A B|=\sqrt{(2-(-2))^2+(4-(-4))^2}=\sqrt{4^2+8^2} \\ & =\sqrt{16+64}=\sqrt{80}=\sqrt{16 \times 5}=4 \sqrt{5} \end{aligned} \]
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