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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 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :
  • a)
    2√3-1
  • b)
    2√3-2
  • c)
    √3-2
  • d)
    √3-1
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
A square, of each side 2, lies above the x-axis and has one vertex at ...
Let's draw the square and label the vertices as A, B, C, and D.

Since one side of the square passes through the origin and makes an angle of 30 degrees with the positive x-axis, we know that this side is aligned with the line y = x * tan(30 degrees) = x/sqrt(3).

Since the side length of the square is 2, the x-coordinate of point A is 2/sqrt(3). Since point A is one of the vertices of the square, it is aligned with the x-axis.

Similarly, since the side length of the square is 2, the y-coordinate of point C is 2/sqrt(3). Since point C is one of the vertices of the square, it is aligned with the y-axis.

Now, let's find the coordinates of points B and D.

Since point B is aligned with the line y = x/sqrt(3), we can substitute x = 2/sqrt(3) into this equation to find the y-coordinate of point B.
y = (2/sqrt(3))/sqrt(3) = 2/3

Since point D is aligned with the line y = x/sqrt(3), we can substitute y = 2/sqrt(3) into this equation to find the x-coordinate of point D.
2/sqrt(3) = x/sqrt(3)
x = 2

So the coordinates of the vertices of the square are:
A: (2/sqrt(3), 0)
B: (2/sqrt(3), 2/3)
C: (0, 2/sqrt(3))
D: (2, 2/sqrt(3))

The sum of the x-coordinates of the vertices of the square is:
(2/sqrt(3)) + (2/sqrt(3)) + 0 + 2 = 4/sqrt(3) + 2 = (4 + 2sqrt(3))/sqrt(3) = (4sqrt(3) + 6)/3

So the correct answer is (4sqrt(3) + 6)/3.
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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 30o with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is :a)2√3-1b)2√3-2c)√3-2d)√3-1Correct answer is option 'C'. Can you explain this answer?
Question Description
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 :a)2√3-1b)2√3-2c)√3-2d)√3-1Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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 :a)2√3-1b)2√3-2c)√3-2d)√3-1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 :a)2√3-1b)2√3-2c)√3-2d)√3-1Correct answer is option 'C'. Can you explain this answer?.
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