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In the rectangular coordinate system, segment OP is rotated
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24 Aug 2019, 01:45
24 Aug 2019, 01:45
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Question Stats:
47% (01:36) correct
52% (01:38) wrong based on 487 sessions
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Attachment:
#GREpracticequestion In the rectangular.png [ 3.79 KiB | Viewed 22624 times ]
In the rectangular coordinate system, segment OP is rotated counterclockwise through an angle of 90° to position OQ (not shown).
Quantity A |
Quantity B |
The x-coordinate of point \(Q\) |
\(-1\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: In the rectangular coordinate system, segment OP is rotated
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01 May 2020, 06:25
01 May 2020, 06:25
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Carcass wrote:
Attachment:
#GREpracticequestion In the rectangular.png
In the rectangular coordinate system, segment OP is rotated counterclockwise through an angle of 90° to position OQ (not shown).
Quantity A |
Quantity B |
The x-coordinate of point \(Q\) |
\(-1\) |
The two given coordinates (√3, 1) should remind us of the special 30-60-90 right triangle.
If we draw a line from the point that is perpendicular to the x-axis, we get a right triangle.
This means we can apply the Pythagorean theorem to determine that the length of the line segment is 2.
At this point, we can see the special 30-60-90 right triangle hiding in the diagram.
When we rotate the line segment 90 degrees, the length of the line segment is still 2.
If we draw a line from the new point to the x-axis, we get another a right triangle.
More importantly, we can see that our new right triangle is also a 30-60-90 right triangle, which means it has the following lengths.
From here we can see that (-1, √3) are the coordinates of the new point.
The x-coordinate of the new point is -1, which means Quantities A and B are equal.
Answer: C
Cheers,
Brent
General Discussion
Re: In the rectangular coordinate system, segment OP is rotated
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25 Aug 2019, 05:38
25 Aug 2019, 05:38
2
since rotation is 90deg counterclockwise
the coordinates of point P(x,y) will become (-y,x) for Q on the new line OQ (rotated line)
i.e if coordinates of P are (x,y) then after 90deg rotation of OP, on line OQ, the coordinates of point Q will be (-y,x)
in this case coordinates of P are (root3,1)
hence Q will have coordinates (-1,root3)
now x coordinate of Q is -1 which is equal to Quantity B
hence the answer is C
the coordinates of point P(x,y) will become (-y,x) for Q on the new line OQ (rotated line)
i.e if coordinates of P are (x,y) then after 90deg rotation of OP, on line OQ, the coordinates of point Q will be (-y,x)
in this case coordinates of P are (root3,1)
hence Q will have coordinates (-1,root3)
now x coordinate of Q is -1 which is equal to Quantity B
hence the answer is C
