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rectangular cartensian co-ordinates — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
If the axes be rotated through an angle $\frac{\pi}{3}$ in the clockwise direction with  respect to $(0, 0)$ the point $(4, 2)$ in the new system was formally-
  • A
    $(2 + \sqrt 3 , -2 \sqrt 3 -1)$
  • B
    $(-2 \sqrt 3 + 1, 2 + \sqrt 3 )$
  • ✓
    $(2 + \sqrt 3 , -2 \sqrt 3 + 1)$
  • D
    $(2 -\sqrt 3 , -2  \sqrt 3 -1)$
✓

Answer

Correct option: C.
$(2 + \sqrt 3 , -2 \sqrt 3 + 1)$
c
  $x$ $y$
$4$ $1/2$ $ - \sqrt 3 /2$
$2$ $\sqrt 3 /2$ $1/2$

$x=4\left(\frac{1}{2}\right)+2\left(\frac{\sqrt{3}}{2}\right)=2+\sqrt{3}$

$y=4\left(-\frac{\sqrt{3}}{2}\right)+2\left(\frac{1}{2}\right)=-2 \sqrt{3}+1$

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