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 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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In the rectangular coordinate system, the line y = x is the [#permalink]

Show Tags

15 May 2012, 21:23

5

This post received KUDOS

8

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

63% (02:22) correct
37% (01:04) wrong based on 397 sessions

HideShow timer Statistics

In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C?

A. (-3;-2) B. (-2; 3) C. (3;-2) D. (2;-3) E. (2; 3)

Given : 1> y = x is the perpendicular bisector of segment AB 2> x = 0 (y-axis) is the perpendicular bisector of segment BC 3> If the coordinates of point A are (3, 2)

Combining 1 and 3, we can deduce that point B is the reflection of point A in the Axis Bisector (y = x) => Coordinates of Point B would be reverse of A and that is (2, 3) Note : here reflection is in X=Y , so x -coordinate and y - coordinate would exchange their places.

So we can say : 4> If the coordinates of point B are (2, 3)

Combining 3 and 4, we can deduce that point C is the reflection of point B in the Y Axis (x = 0) line => Coordinates of Point C would be reverse of B and that is (-2, 3) Note : here reflection is in Y axis , so sign of x -coordinate would change while sign of y coordinate would remain same.

In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C?

A. (-3;-2) B. (-2; 3) C. (3;-2) D. (2;-3) E. (2; 3)

Since the line y=x is the perpendicular bisector of segment AB, then point B is the mirror reflection of point A around the line y=x, so its coordinates are (2, 3). The same way, since the y-axis is the perpendicular bisector of segment BC then the point C is the mirror reflection of point B around the y-axis, so its coordinates are (-2, 3).

Answer: B.

The question becomes much easier if you just draw a rough sketch:

Attachment:

Point C.png [ 13.36 KiB | Viewed 8745 times ]

Now, you can simply see that options A, C, and D (blue dots) just can not be the right answers. As for option E: point (2, 3) coincides with point B, so it's also not the correct answer. Only answer choice B remains.

@Bunuel : Isn't thr an algebric way to solve this problem ?

Sure there is but the solution above is less time consuming.

Coordinate Geometry chapter of Math Book (coordinate-geometry-87652.html) could help you to figure out algebraic solution if still needed.
_________________

(I am trying to solve this using substitution, not thinking of it in terms of reflection across lines)

In a rectangular coordinate system, the line y=x is the perpendicular bisector of segment AB and the x-axis is the perpendicular bisector of segment BC. If the coordinates of point A are (2,3), what are the coordinates of point C?

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

(I am trying to solve this using substitution, not thinking of it in terms of reflection across lines)

In a rectangular coordinate system, the line y=x is the perpendicular bisector of segment AB and the x-axis is the perpendicular bisector of segment BC. If the coordinates of point A are (2,3), what are the coordinates of point C?

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

Merging topics. Please ask if anything remains unclear.

Re: In the rectangular coordinate system, the line y = x is the [#permalink]

Show Tags

31 Aug 2012, 10:59

enigma123 wrote:

In the rectangular coordinate system, the line y = x is the perpendicular bisector of segment AB (not shown), and the y-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (3; 2), what are the coordinates of point C?

A. (-3;-2) B. (-2; 3) C. (3;-2) D. (2;-3) E. (2; 3)

Hey enigma123,

An alternate way of solving this would be by visualization.

First, we plot the line y=x and the point A(3,2) in our graph. a) Since we are given that AB is the perpendicular bisector of the line y=x, we can deduce from the figure that the value of the 'x' co-ordinate of point B must be positive and less than the value of the 'x' co-ordinate of point A. From this we can eliminate choices A,B and C b) Also, we can deduce by observation that the 'y' co-ordinate of point B is positive (since B lies above the X axis) From this we can eliminate choice D

From a) and b), we now know that point B lies in the first quadrant.

Re: In the rectangular coordinate system, the line y = x is the [#permalink]

Show Tags

27 Jun 2014, 07:20

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: In the rectangular coordinate system, the line y = x is the [#permalink]

Show Tags

22 Aug 2015, 01:05

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: In the rectangular coordinate system, the line y = x is the [#permalink]

Show Tags

12 Sep 2016, 23:40

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.
_________________

Best Schools for Young MBA Applicants Deciding when to start applying to business school can be a challenge. Salary increases dramatically after an MBA, but schools tend to prefer...

Marty Cagan is founding partner of the Silicon Valley Product Group, a consulting firm that helps companies with their product strategy. Prior to that he held product roles at...