TS EAMCET · Maths · Straight Lines
The co-ordinate axes are rotated through an angle \(135^{\circ}\). If the co-ordinates of a point \(P\) in the new system are known to be \((4,-3)\), then the co-ordinates of \(P\) in the original system are
- A \(\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
- B \(\left(\frac{1}{\sqrt{2}},-\frac{7}{\sqrt{2}}\right)\)
- C \(\left(-\frac{1}{\sqrt{2}},-\frac{7}{\sqrt{2}}\right)\)
- D \(\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(-\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
Let \(\left(x_1, y_1\right)\) be the co-ordinate of new system, then \(x_1=x \cos \theta+y \sin \theta\) \(y_1=-x \sin \theta+y \cos \theta\) Given that \(\left(x_1, y_1\right)=(4,-3)\) and \(\theta=135^{\circ}\) \(4=x \cos 135^{\circ}+y \sin 135^{\circ}\)…
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