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

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSrectangular cartensian co-ordinates1 Mark
MCQ
A square, of each side $2$, lies above the $x-$ axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle $30^o$ with the positive direction of the $x-$ axis, then the sum of the $x$ coordinates of the vertices of the square is
  • A
    $2\sqrt 3  - 1$
  • ✓
    $2\sqrt 3  - 2$
  • C
    $\sqrt 3  - 2$
  • D
    $\sqrt 3  - 1$
✓

Answer

Correct option: B.
$2\sqrt 3  - 2$
b
$\frac{x}{{\cos \,{{30}^o}}} = \frac{y}{{\sin \,{{30}^o}}}$

$x = \sqrt 3 $

$y = 1$

$\frac{x}{{\cos \,{{120}^o}}}\frac{y}{{\sin \,{{120}^o}}} = 2$

$x =  - 1,y = \sqrt 3 $

$\frac{x}{{\cos \,{{75}^o}}} = \frac{y}{{\sin \,{{75}^o}}} = 2\sqrt 2 $

$x = \sqrt 3  - 1$

$y = \sqrt 3  + 1$

Sum $ = 2\sqrt 3  - 2$

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