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In the rectangular coordinate system, segment OP is rotated

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Carcass
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In the rectangular coordinate system, segment OP is rotated [#permalink] New post   24 Aug 2019, 01:45
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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.

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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   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.
Image


When we rotate the line segment 90 degrees, the length of the line segment is still 2.
Image


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.
Image

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
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   25 Aug 2019, 05:38
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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
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   27 Apr 2020, 02:49
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Darpan wrote:
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

Ok I kinda remember the rules of mirroring from physics but In application I cannot understand why x and y will be switched.

since just its -ve of x and nothing else is changed
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   27 Apr 2020, 23:08
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Darpan wrote:
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


Since it is rotated counterclockwise (opposite direction to clockwise direction), the coordinates of OQ will be (-x,y) and not (-y,x). The current value of x is sqt3, which is equal to 1.732. Thus, new coordinates of x will be -1.732, which is less than -1. Thus, the answer should be B.
If the question asked about the y-coordinate, then the answer will be C.
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   30 Apr 2020, 05:20
prototypevenom wrote:
Darpan wrote:
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

Ok I kinda remember the rules of mirroring from physics but In application I cannot understand why x and y will be switched.

since just its -ve of x and nothing else is changed


Please clarify, I have the same doubt
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   30 Apr 2020, 23:08
WillESP2 wrote:
prototypevenom wrote:
Darpan wrote:
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

Ok I kinda remember the rules of mirroring from physics but In application I cannot understand why x and y will be switched.

since just its -ve of x and nothing else is changed


Please clarify, I have the same doubt

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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   01 May 2020, 12:29
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Great explanation Sir
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   17 Jun 2021, 09:43
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Since OP is rotated counterclockwise through an angle 90 degree, which is OQ. Hence OP & OQ are perpendicular to each other.As a result the slope of line OP= 1/√3 and line OQ=-√3/1. Therefore X coordinate of point Q is -1.

Answer C
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In the rectangular coordinate system, segment OP is rotated [#permalink] New post   14 Jul 2022, 02:51
GreenlightTestPrep wrote:
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.
Image


When we rotate the line segment 90 degrees, the length of the line segment is still 2.
Image


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.
Image

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


Sir, a great explanation in the first place! But, still I'm not able to understand completely. When rotated 90 degrees, how did the corresponding angles 30 and 60 interchange? Can you explain the thought process behind this?
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   14 Jul 2022, 06:20
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SivhHarish wrote:
Sir, a great explanation in the first place! But, still I'm not able to understand completely. When rotated 90 degrees, how did the corresponding angles 30 and 60 interchange? Can you explain the thought process behind this?


First, I used the fact that angles on a line add up to 180°.
We already had two angles (90° and 30°), which means the remaining angle must be 60°.

Does that help?
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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   19 Jan 2023, 04:22
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Might be useful for easy rotations:

90° clockwise rotation: (x,y) becomes (y,-x)

90° counterclockwise rotation: (x,y) becomes (-y,x)

180° clockwise and counterclockwise rotation: (x, y) becomes (-x,-y)

270° clockwise rotation: (x,y) becomes (-y,x)

270° counterclockwise rotation: (x,y) becomes (y,-x)

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Re: In the rectangular coordinate system, segment OP is rotated [#permalink] New post   03 Apr 2024, 07:01
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