AP EAMCET · Maths · Straight Lines
Find the coordinates of \(M\) in the original system if the point \(M\) changes to \((4,-3)\) when the axes are rotated through an angle of \(135^{\circ}\).
- A \(\left(\frac{-1}{2}, \frac{7}{2}\right)\)
- B \(\left(\frac{1}{2}, \frac{7}{2}\right)\)
- C \(\left(\frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
- D \(\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
Answer & Solution
Correct Answer
(C) \(\left(\frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
Step-by-step Solution
Detailed explanation
\[ \begin{aligned} (*) \text { Let } M^{\prime}=(4,-3) & =\left(x^{\prime}, y^{\prime}\right) \\ \theta & =135^{\circ} \end{aligned} \] Let coordinates of \(M\) be \((x, y)\) we have,…
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