TS EAMCET · Maths · Straight Lines
The origin is translated to \((1,2)\). The point \((7,5)\) in the old system undergoes the following transformations successively. I. Moves to the new point under the given translation of origin. II. Translated through 2 units along the negative direction of the new \(X\)-axis. III. Rotated through an angle \(\frac{\pi}{4}\) about the origin of new system in the clockwise direction. The final position of the point \((7,5)\) is
- A \(\left(\frac{9}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
- B \(\left(\frac{7}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
- C \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
- D \(\left(\frac{5}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{7}{\sqrt{2}}, \frac{-1}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
Under the translation of origin to \((1,2)\) the point \((7,5)\) undergoes to \((7-1,5-2) \equiv(6,3)\) Under the translation through 2 units along the negative direction of the new \(x\)-axis, the point \((6,3)\) undergoes to \((6-2,3) \equiv(4,3)\) Under the rotation throw an…
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