TS EAMCET · Maths · Straight Lines
( \(a, b\) ) are the new coordinates of the point \((2,3)\) after shifting the origin to the point \((3,2)\) by translation of axes. If \((c, d)\) are the new coordinates of the point \((a, b)\) after rotating the axes through an angle \(\frac{\pi}{4}\) about the origin in the anti-clockwise direction, then \(d-c=\)
- A \(0\)
- B \(1\)
- C \(\sqrt{2}\)
- D \(2 \sqrt{2}\)
Answer & Solution
Correct Answer
(C) \(\sqrt{2}\)
Step-by-step Solution
Detailed explanation
\(a = 2 - 3 = -1\) \(b = 3 - 2 = 1\) \(c = a \cos \frac{\pi}{4} - b \sin \frac{\pi}{4} = (-1)\frac{1}{\sqrt{2}} - (1)\frac{1}{\sqrt{2}} = -\frac{2}{\sqrt{2}} = -\sqrt{2}\) \(d = a \sin \frac{\pi}{4} + b \cos \frac{\pi}{4} = (-1)\frac{1}{\sqrt{2}} + (1)\frac{1}{\sqrt{2}} = 0\)…
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