AP EAMCET · Maths · Straight Lines
If the axes are rotated through an angle \(45^{\circ}\) in the positive direction without changing the origin, then the co-ordinates of the point \((\sqrt{2}, 4)\) in the old system are
- A \((1-2 \sqrt{2}, 1+2 \sqrt{2})\)
- B \((1+2 \sqrt{2}, 1-2 \sqrt{2})\)
- C \((2 \sqrt{2}, \sqrt{2})\)
- D \((\sqrt{2}, 2)\)
Answer & Solution
Correct Answer
(A) \((1-2 \sqrt{2}, 1+2 \sqrt{2})\)
Step-by-step Solution
Detailed explanation
If \(\theta\) is the angle of rotation, then the co-ordinates in the new system are \(x^{\prime}=x \cos \theta+y \sin \theta\), \(y^{\prime}=y \cos \theta-x \sin \theta\) Given that \(x^{\prime}=\sqrt{2}, y^{\prime}=4\) Thus, \(x \cos \theta+y \sin \theta=\sqrt{2}\)…
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