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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)


  • Option 4)



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))



Option 1)

2\sqrt{3} -1

This option is correct

Option 2)

2\sqrt{3} -2

This option is incorrect

Option 3)


This option is incorrect

Option 4)


This option is incorrect

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