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TS EAMCET · Maths · Straight Lines

When the origin is shifted to \((1,-2)\) by translation of coordinate axes, the transformed coordinates of \((3,-2)\) are \((\alpha, \beta)\). If the axes are rotated about origin through an angle of \(45^{\circ}\) after the translation, then the transformed coordinates of \((\alpha, \beta)\) are

  1. A \((\sqrt{2}, 0)\)
  2. B \((0, \sqrt{2})\)
  3. C \((-\sqrt{2}, \sqrt{2})\)
  4. D \((\sqrt{2},-\sqrt{2})\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((\sqrt{2},-\sqrt{2})\)

Step-by-step Solution

Detailed explanation

Given, \[ \begin{aligned} & (h, k) \equiv(1,-2) \text { and }(x, y)=(3,-2) \\ \therefore & \alpha=x-h \text { and } \beta=y-k \\ \therefore & (\alpha, \beta) \equiv(2,0) \end{aligned} \] Axes rotated about origin through an angle of \(45^{\circ}\) \(\therefore\) New coordinate…