Last visit was: 05 Nov 2024, 21:30 It is currently 05 Nov 2024, 21:30

Close

GRE Prep Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GRE score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel
Verbal Expert
Joined: 18 Apr 2015
Posts: 29894
Own Kudos [?]: 36131 [38]
Given Kudos: 25919
Send PM
Most Helpful Community Reply
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [38]
Given Kudos: 136
Send PM
General Discussion
avatar
Intern
Intern
Joined: 24 Aug 2019
Posts: 30
Own Kudos [?]: 10 [2]
Given Kudos: 0
Send PM
avatar
Intern
Intern
Joined: 17 Jan 2020
Posts: 30
Own Kudos [?]: 55 [2]
Given Kudos: 0
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
2
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
Attachments

Screenshot_1.jpg
Screenshot_1.jpg [ 40.78 KiB | Viewed 22879 times ]

avatar
Manager
Manager
Joined: 09 Mar 2020
Posts: 164
Own Kudos [?]: 201 [3]
Given Kudos: 0
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
3
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.
avatar
Intern
Intern
Joined: 26 Apr 2020
Posts: 14
Own Kudos [?]: 11 [0]
Given Kudos: 0
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
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
avatar
Intern
Intern
Joined: 17 Jan 2020
Posts: 30
Own Kudos [?]: 55 [0]
Given Kudos: 0
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
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

@carcass?
Verbal Expert
Joined: 18 Apr 2015
Posts: 29894
Own Kudos [?]: 36131 [0]
Given Kudos: 25919
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
Expert Reply
Great explanation Sir
Intern
Intern
Joined: 30 Oct 2020
Posts: 2
Own Kudos [?]: 3 [3]
Given Kudos: 101
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
3
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
Manager
Manager
Joined: 01 Apr 2022
Posts: 65
Own Kudos [?]: 15 [0]
Given Kudos: 79
Send PM
In the rectangular coordinate system, segment OP is rotated [#permalink]
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?
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Own Kudos [?]: 12176 [1]
Given Kudos: 136
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
1
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?
avatar
Intern
Intern
Joined: 02 Jun 2022
Posts: 3
Own Kudos [?]: 6 [2]
Given Kudos: 5
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
2
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)

Posted from my mobile device
User avatar
GRE Prep Club Legend
GRE Prep Club Legend
Joined: 07 Jan 2021
Posts: 5006
Own Kudos [?]: 74 [0]
Given Kudos: 0
Send PM
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Prep Club for GRE Bot
Re: In the rectangular coordinate system, segment OP is rotated [#permalink]
Moderators:
GRE Instructor
77 posts
GRE Forum Moderator
37 posts
Moderator
1111 posts
GRE Instructor
233 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne