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 300 with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square

  • Option 1)

    2\sqrt{3} -1

  • Option 2)

    2\sqrt{3} -2

  • Option 3)

    \sqrt{3}-2

  • Option 4)

    \sqrt{3}-1

 

Answers (1)

As we learnt in

Parametric form -

x=x_{1}+r\cos \Theta

y=y_{1}+r\sin \Theta

- wherein

Where \Theta  is the inclination of the line and r is the distance between (x,y)  and (x_{1},y_{1})

 x-coordinates of A is 2cos30^{\circ}

=2\times \frac{\sqrt{3}}{2}=\sqrt{3}

angle of OB with positive x-axis is 30^{\circ}+45^{\circ}=75^{\circ}

Hence x - coordinate of B is 2\sqrt{2}\cos75^{\circ}

=2\sqrt{2}\left ( \frac{\sqrt{3}-1}{2\sqrt{2}} \right ) =(\sqrt{3}-1)

x-cordinate of C is -2sin30^{\circ}=-1

Hence Sum=(\sqrt{3}+\sqrt{3}-1+(-1))

=2\sqrt{3}-2

 


Option 1)

2\sqrt{3} -1

This option is correct

Option 2)

2\sqrt{3} -2

This option is incorrect

Option 3)

\sqrt{3}-2

This option is incorrect

Option 4)

\sqrt{3}-1

This option is incorrect

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 24999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions