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AP EAMCET · Maths · Straight Lines

Let \(\mathrm{A}=(2,0)\) and \(\mathrm{B}=(6,4)\) be two points. If \(\overline{A B}\) is rotated about \(\mathrm{A}\) through an angle of \(45^{\circ}\) in the negative direction, then the co-ordinates of \(\mathrm{B}\) after the rotation are

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

Answer & Solution

Correct Answer

(A) \((2+4 \sqrt{2}, 0)\)

Step-by-step Solution

Detailed explanation

\( \mathrm{B'} = \mathrm{B} - \mathrm{A} = (6-2, 4-0) = (4,4) \) \( \mathrm{B''_{x}} = 4 \cos(-45^\circ) - 4 \sin(-45^\circ) = 4(\frac{1}{\sqrt{2}}) - 4(-\frac{1}{\sqrt{2}}) = 4\sqrt{2} \)…