AP EAMCET · Maths · Straight Lines

If $S_{1}$ and $S_{2}$ are two straight lines such that the reflection of $S_{1}$ in $S_{2}$ and the reflection of $S_{2}$ in $S_{1}$ coincide, the angle between $S_{1}$ and $S_{2}$ is equal to?

A $\frac{π}{3}$
B $\frac{π}{6}$
C $\frac{π}{4}$
D Data is insufficient.

Verified Solution

Answer & Solution

Correct Answer

(A) $\frac{π}{3}$

Step-by-step Solution

Detailed explanation

According to the above figure, S1 and S'1 are the reflection of each other in S2. And S2 and S'2 are the reflection of each other in S1. So, S'1 and S'2 are coincide. ⇒3θ=π ⇒θ=π3

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If S1 and S2 are two straight lines such that the reflection of S1 in S2 and the reflection of S2 in S1 coincide, the angle between S1 and S2 is equal to?

Step-by-step Solution

If $S_{1}$ and $S_{2}$ are two straight lines such that the reflection of $S_{1}$ in $S_{2}$ and the reflection of $S_{2}$ in $S_{1}$ coincide, the angle between $S_{1}$ and $S_{2}$ is equal to?