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QJEEM17Ma731d: JEE Main 2017 Mathematics - Class 11 JEEM17Ma731d Solution: A square, of each side 2, lies above the x-axis and has one…

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 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :

Multiple Choice Options

  • A 23−12\sqrt 3 - 1
  • B 23−22\sqrt 3 - 2
  • C 3−2\sqrt 3 - 2
  • D 3−1\sqrt 3 - 1

Step-by-Step Verified Solution

JEE Main 2017 (Online) 9th April Morning Slot Mathematics - Straight Lines and Pair of Straight Lines Question 119 English Explanation

Let, coordinate of point A = (x, y).

∴   \therefore\,\,\, For point A,

xcos⁡30∘{x \over {\cos {{30}^ \circ }}} = ysin⁡30∘{y \over {\sin {{30}^ \circ }}} = 2

⇒\Rightarrow x = 3\sqrt 3

and y = 1

Similarly, For point B,

xcos⁡75∘{x \over {\cos {{75}^ \circ }}} = ysin⁡75∘{y \over {\sin {{75}^ \circ }}} = 2 2\sqrt 2

∴   \therefore\,\,\, x = 3−1\sqrt 3 - 1

y = 3+1\sqrt 3 + 1

For point C,

xcos120∘{x \over {cos{{120}^ \circ }}} = ysin120∘{y \over {sin{{120}^ \circ }}} = 2

⇒\Rightarrow    \,\,\, x = −- 1

y = 3\sqrt 3

∴   \therefore\,\,\, Sum of the x - coordinate of the vertices

= 0 + 3\sqrt 3 + 3\sqrt 3 −- 1 + ( −- 1) = 2 3\sqrt 3 −- 2

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