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JEE Main 20179 AprilOnline
Exam
JEE Main
Year
2017
Date
9 April
Mode
Online
Subject
Mathematics
Chapter
Straight Lines

JEE Main 2017 · 9 April · Online · Mathematics · Straight Lines

A square, of each side 2 , lies above the x -axis and has one...

A square, of each side 22, lies above the xx-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30°30 ° with the positive direction of the xx-axis , then the sum of the xx-coordinates of the vertices of the square is: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

Options

  1. A23−22\sqrt{3} - 2
  2. B3−2\sqrt{3} - 2
  3. C23−12\sqrt{3} - 1
  4. D3−1\sqrt{3} - 1

Correct answer

A. 23−22\sqrt{3} - 2

Step-by-step solution

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

For A,A,

\dfrac{x}{\cos 30 °} = \dfrac{y}{\sin 30 °} = 2

→x=232=3\to x = \dfrac{2\sqrt{3}}{2} = \sqrt{3} and y=1y = 1

For C,C,

\dfrac{x}{\cos 120 °} = \dfrac{y}{\sin 120 °} = 2

x=−1,y=3x = - 1, y = \sqrt{3}

For B,B,

\dfrac{x}{\cos 75 °} = \dfrac{y}{\sin 75 °} = 2\sqrt{2}

x=3−1x = \sqrt{3} - 1, y=3+1y = \sqrt{3} + 1

Sum of the xx-coordinates =0+3+3−1+(−1)= 0 + \sqrt{3} + \sqrt{3} - 1 + \left(- 1\right)

=23−2= 2\sqrt{3} - 2

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