TS EAMCET · Maths · Straight Lines
The point \((4,1)\) undergoes the following transformations successively I. Reflection about the line \(y=x\) II. Translation through a distance 2 units in the direction of positive \(X\)-axis. III. Rotation through an angle \(\frac{\pi}{4}\) about origin in the anticlockwise direction. Then, the final position of the point is
- A \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
- B \((\sqrt{2}, 7 \sqrt{2})\)
- C \((-\sqrt{2}, 7 \sqrt{2})\)
- D \(\left(\frac{1}{\sqrt{2}},-\frac{7}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(A) \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
We have, Given point \((4,1)\). When \((4,1)\) is reflected about line \(y=x\), the new coordinates become \((1,4)\). Again \((1,4)\) is translated through a distance 2 units in the direction of positive \(X\)-axis, the new coordinates become \((1+2,4+0)\) i.e. \((3,4)\). Lastly…
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