TS EAMCET · Maths · Straight Lines
If the point \(P(1,3)\) undergoes the following transformations successively. (i) Reflection with respect to the line \(y=x\). (ii) Translation through 3 units along the positive direction of the \(X\)-axis. (iii) Rotation through an angle of \(\frac{\pi}{6}\) about the origin in the clockwise direction. Then, the final position of the point \(P\) is
- A \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
- B \(\left(\frac{\sqrt{7}}{2}, \frac{-5}{\sqrt{2}}\right)\)
- C \(\left(\frac{6+\sqrt{3}}{2}, \frac{1-6 \sqrt{3}}{2}\right)\)
- D \(\left(\frac{6+\sqrt{3}-1}{2}, \frac{6+\sqrt{3}}{2}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{6 \sqrt{3}+1}{2}, \frac{\sqrt{3}-6}{2}\right)\)
Step-by-step Solution
Detailed explanation
The reflection of the point \(P(1,3)\) about the line \(y=x\) is \(Q(3,1)\) After translation through a distance 3 units along the positive direction of \(X\)-axis at the point whose coordinate are \(R(6,1)\). After rotation through an angle of \(\frac{\pi}{6}\) about the origin…
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