Last visit was: 14 Jul 2024, 06:07 It is currently 14 Jul 2024, 06:07
Toolkit
GMAT 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

every week, we’ll send you an estimated GMAT 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.

# The point (-3, 2) is rotated 90° clockwise around the origin to point

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94342
Own Kudos [?]: 640681 [10]
Given Kudos: 85011
Senior Manager
Joined: 25 Feb 2019
Posts: 279
Own Kudos [?]: 222 [0]
Given Kudos: 32
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 7963
Own Kudos [?]: 4214 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5275
Own Kudos [?]: 4178 [2]
Given Kudos: 160
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: The point (-3, 2) is rotated 90° clockwise around the origin to point [#permalink]
2
Kudos
Bunuel wrote:
The point (-3, 2) is rotated 90° clockwise around the origin to point B. Point B is then reflected over the line x = y to point C. What are the coordinates of C?

(A) (-3, -2)
(B) (-2, -3)
(C) (2, -3)
(D) (2, 3)
(E) (3, 2)

Given: The point (-3, 2) is rotated 90° clockwise around the origin to point B. Point B is then reflected over the line x = y to point C.
Asked: What are the coordinates of C?

Attachment:

Screenshot 2020-07-14 at 10.49.02 AM.png [ 26.13 KiB | Viewed 21447 times ]

IMO E
VP
Joined: 10 Jul 2019
Posts: 1385
Own Kudos [?]: 576 [0]
Given Kudos: 1656
The point (-3, 2) is rotated 90° clockwise around the origin to point [#permalink]
Reflection 1:

The way I understood 90 degree rotations was by the “tipping the rectangle” method.

It sounds goofy, but:

Since we are rotating 90 degrees about the Origin (0 , 0) ——> make a rectangle with these 2 points

Label (-3 , 2) as point A and Origin as Point O

If we join the horizontal and vertical lines to the Y and X axis, respectively, we end up with a rectangle that is 3 units along the Negative X Axis and 2 units along the Positive Y Axis

Now imagine lifting the rectangle up and pushing it from quadrant 2 into quadrant 1 - i.e, a 90 degree rotation clockwise about the Origin

This would give us a rectangle of 2 units along the positive X axis and 3 units along positive Y axis. Point A would now move to the upper right corner of this new rectangle that we pushed over ———> this will be point (2 , 3)

You can confirm visually by:

-connecting original point A at (-3 ,2) with the Origin

-and connecting new image point A at (2 , 3)

these 2 points and the origin will create a 90 degree angle about the Origin (both lines are diagonals of their respective rectangles)

Or, the explanation is too long winded, you can follow the Rule:

For 90 degree rotations clockwise about the Origin: (X , Y) ———>becomes image point of (Y , -X)

(-3 ,2) becomes (2, 3)

So the first rotation gives us point (2 , 3)

Reflection 2:

Line Y = X is the Line that passes through the origin and creates a 45 degree angle with the X axis

The original point of (2 , 3) and the Image Point will always be equidistant from the Mirror Line over which the original point is reflected.

To visualize it in this problem:

(2 ,2) and (3 , 3) are both on line Y = X

Point (2 , 3) will be +1 unit above (2 ,2) and + 1 unit to the left of (3 , 3)

This creates a right triangle with sides of 1 and 1

To find the image point reflected over Y = X, we make the opposite moves from these points (reversed) on Line Y = X:

from (2 , 2) we move 1 unit to the right: X coordinate = 3

From (3 , 3) we move 1 unit down: Y coordinate = 2

Final Point is (3 , 2)

Or the rule:

Reflecting point (X , Y) over the line given by Y = X ————> image point will be (Y , X)

In other words, just rearrange the coordinates

Posted from my mobile device
Tutor
Joined: 16 Oct 2010
Posts: 15108
Own Kudos [?]: 66621 [2]
Given Kudos: 436
Location: Pune, India
Re: The point (-3, 2) is rotated 90° clockwise around the origin to point [#permalink]
2
Bookmarks
Bunuel wrote:
The point (-3, 2) is rotated 90° clockwise around the origin to point B. Point B is then reflected over the line x = y to point C. What are the coordinates of C?

(A) (-3, -2)
(B) (-2, -3)
(C) (2, -3)
(D) (2, 3)
(E) (3, 2)

We have discussed this concept in detail here:

When the point (-3, 2) is rotated clockwise 90 degrees, the point lies in first quadrant and co-ordinates of x and y flip. So you get the point (2, 3).

When you reflect (2, 3) over the line x = y, this is like having a square with one vertex at (2, 3), one at (2, 2), one at (3, 3) so the fourth vertex will be at (3, 2).

Non-Human User
Joined: 09 Sep 2013
Posts: 33966
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: The point (-3, 2) is rotated 90° clockwise around the origin to point [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT 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.
Re: The point (-3, 2) is rotated 90° clockwise around the origin to point [#permalink]
Moderator:
Math Expert
94342 posts