TS EAMCET · Maths · Straight Lines
The point \(P(1,4)\) occupies the positions \(A, B\) and \(C\) respectively after undergoing the following three transformation successively. I. Reflection about the line \(y=x\). II. Translation through a distance of 1 unit along the positive direction of \(X\)-axis. III. Rotation of the line \(O B\) through an angle \(\frac{\pi}{4}\) about the origin in the anti-clockwise direction. Then, the coordinates of \(C\) are
- A \((\sqrt{2}, 2 \sqrt{2})\)
- B \((2 \sqrt{2}, 3 \sqrt{2})\)
- C \(\left(\frac{5}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
- D \(\left(\frac{2}{\sqrt{2}}, \frac{3}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(B) \((2 \sqrt{2}, 3 \sqrt{2})\)
Step-by-step Solution
Detailed explanation
Reflection of point \(P(1,4)\) about the line \(y=x\) is \(A(4,1)\). Now, after translation of point \(A(4,1)\) through a distance of 1 unit along the positive direction of \(X\)-axis, the new coordinate is \(B(5,1)\). Now, after rotation of the line \(O B\) through an angle…
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