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 ° with the positive direction of the x -axis , then

Question

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

TestHub · Accepted Answer

For A , x cos 30 ° = y sin 30 ° = 2 ⇒ x = 2 3 2 = 3 and y = 1 For C , x cos 120 ° = y sin 120 ° = 2 x = - 1 , y = 3 For B , x cos 75 ° = y sin 75 ° = 2 2 x = 3 - 1 , y = 3 + 1 Sum of the x -coordinates = 0 + 3 + 3 - 1 + - 1 = 2 3 - 2

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