ExamBro
ExamBro
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 \(135^{\circ}\).

  1. A \(\left(\frac{-1}{2}, \frac{7}{2}\right)\)
  2. B \(\left(\frac{1}{2}, \frac{7}{2}\right)\)
  3. C \(\left(\frac{-1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)\)
  4. D \(\left(\frac{1}{\sqrt{2}}, \frac{7}{\sqrt{2}}\right)\)
Verified Solution

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,…