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In the coordinate system above, line segment OR is rotated clockwise t
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08 Dec 2022, 11:37
08 Dec 2022, 11:37
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47% (01:42) correct
52% (01:46) wrong based on 40 sessions
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GRE In the coordinate system above, line segment OR .jpg [ 14.2 KiB | Viewed 3372 times ]
In the coordinate system above, line segment OR is rotated clockwise through an angle of 120° to position OS (not shown).
Quantity A |
Quantity B |
The x-coordinate of point S |
\(\sqrt{3}\) |
A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.
Re: In the coordinate system above, line segment OR is rotated clockwise t
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11 Dec 2022, 04:00
11 Dec 2022, 04:00
Expert Reply
OE
Drawing a horizontal line from point R to the positive y-axis forms a right triangle. The length of the leg that sits on the y-axis is \(\sqrt{3}\), and the horizontal leg you just drew has length 1. The ratio of the legs is 1 to \(\sqrt{3}\), so you have a 30-60-90 right triangle. Therefore, the hypotenuse (OR) has length 2, and the angle between OR and the positive y-axis is 30 degrees. The first quadrant includes 90 degrees total, so rotating OR 120 degrees clockwise puts OS on the positive x-axis, with a length of 2. Therefore, the x-coordinate of OS is 2, which is slightly larger than \(\sqrt{3}\), which is approximately 1.7. The answer is choice (A).
Drawing a horizontal line from point R to the positive y-axis forms a right triangle. The length of the leg that sits on the y-axis is \(\sqrt{3}\), and the horizontal leg you just drew has length 1. The ratio of the legs is 1 to \(\sqrt{3}\), so you have a 30-60-90 right triangle. Therefore, the hypotenuse (OR) has length 2, and the angle between OR and the positive y-axis is 30 degrees. The first quadrant includes 90 degrees total, so rotating OR 120 degrees clockwise puts OS on the positive x-axis, with a length of 2. Therefore, the x-coordinate of OS is 2, which is slightly larger than \(\sqrt{3}\), which is approximately 1.7. The answer is choice (A).
Re: In the coordinate system above, line segment OR is rotated clockwise t
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21 Sep 2025, 00:27
21 Sep 2025, 00:27
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