It is currently 17 Oct 2017, 21:15

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# In the rectangular coordinate system above, the line y = x

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178

Kudos [?]: 3460 [7], given: 0

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

### Show Tags

27 Dec 2012, 05:05
7
KUDOS
30
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (01:35) correct 31% (02:00) wrong based on 1169 sessions

### HideShow timer Statistics

Attachment:

Reflcetion.png [ 8.39 KiB | Viewed 11887 times ]
In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). 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)
[Reveal] Spoiler: OA

Kudos [?]: 3460 [7], given: 0

Math Expert
Joined: 02 Sep 2009
Posts: 41876

Kudos [?]: 128627 [7], given: 12180

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

### Show Tags

27 Dec 2012, 05:13
7
KUDOS
Expert's post
24
This post was
BOOKMARKED

In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). 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)

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 (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

The same way, since the x-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 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

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

Reflection2.png [ 10.75 KiB | Viewed 11373 times ]
Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

Hope it helps.
_________________

Kudos [?]: 128627 [7], given: 12180

Intern
Joined: 04 Aug 2013
Posts: 6

Kudos [?]: 5 [4], given: 8

Concentration: Sustainability, Entrepreneurship
WE: Architecture (Energy and Utilities)
Re: In the rectangular coordinate system above, the line y = x [#permalink]

### Show Tags

30 Oct 2013, 06:25
4
KUDOS
From question stem, we can know that, Point C will be in the 4th quadrant (X,-Y), which comes down to option C&D.
B is perpendicular to A (2,3). Hence co-ordinates of B will be (3,2).
C & B are parallel to Y-axis and are on the same line. Hence co-ordinates of C will share same X-co-ordinate. (3,-Y). i.e. Ans. choice D

*I have difficult time understanding Co-ordiante geometry, hence try to solve in the simple way. This was my approach and was able to get ans. in less than a Minute.

Kudos [?]: 5 [4], given: 8

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16759

Kudos [?]: 273 [0], given: 0

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

### Show Tags

09 Dec 2014, 10:46
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.
_________________

Kudos [?]: 273 [0], given: 0

Intern
Joined: 17 May 2012
Posts: 46

Kudos [?]: 12 [1], given: 126

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

### Show Tags

16 Feb 2015, 11:03
1
KUDOS
Quote:
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 (-3, 2)

Hi Bunuel,

Isn't x-axis a perpendicular bisector of line BC and the coordinates of C are (3,-2). Looks like some typos in the explanation?

Thanks,
AJ

Kudos [?]: 12 [1], given: 126

Math Expert
Joined: 02 Sep 2009
Posts: 41876

Kudos [?]: 128627 [1], given: 12180

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

### Show Tags

16 Feb 2015, 11:12
1
KUDOS
Expert's post
aj0809 wrote:
Quote:
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 (-3, 2)

Hi Bunuel,

Isn't x-axis a perpendicular bisector of line BC and the coordinates of C are (3,-2). Looks like some typos in the explanation?

Thanks,
AJ

Yes. Edited the typo. Thank you.
_________________

Kudos [?]: 128627 [1], given: 12180

Intern
Joined: 15 Feb 2015
Posts: 13

Kudos [?]: 5 [0], given: 1

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

### Show Tags

16 Feb 2015, 20:27
For this question, I am confused. where do I get the position of B and C?
Thanks ...

Kudos [?]: 5 [0], given: 1

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7671

Kudos [?]: 17339 [2], given: 232

Location: Pune, India
Re: In the rectangular coordinate system above, the line y = x [#permalink]

### Show Tags

17 Feb 2015, 20:06
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
cherryli2015 wrote:
For this question, I am confused. where do I get the position of B and C?
Thanks ...

First of all, this question is not very easy. You should be able to visualize a concept which is not very intuitive to most of us but there are a few OG questions on it. I suggest you to read up on it in the following two posts:
http://www.veritasprep.com/blog/2013/04 ... ry-part-i/
http://www.veritasprep.com/blog/2013/04 ... y-part-ii/

Now, coming back to this question, you are given data to find the positions of B and C.

"the line y = x is the perpendicular bisector of segment AB (not shown)"

You know that point A is (2, 3). We need the mirror image of A on y = x. Imagine drawing a line perpendicular to y = x from A. It will intersect y = x at (2.5, 2.5), a point 0.5 below and 0.5 to the right. So the point B will be 0.5 further to the right and 0.5 down giving us the coordinate (2.5 + .5, 2.5 - .5) i.e. (3, 2).

For C, you are given that
" the x-axis is the perpendicular bisector of segment BC (not shown)"

A line perpendicular to x axis will be x = 0 i.e. vertical line. So C's x coordinate will be the same as B's x coordinate. Since B is 2 above the x axis, C will be 2 below the x axis. So C will be at (3, -2)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17339 [2], given: 232

Director
Joined: 10 Mar 2013
Posts: 593

Kudos [?]: 459 [0], given: 200

Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
In the rectangular coordinate system above, the line y = x [#permalink]

### Show Tags

16 Jul 2015, 06:01
YX is bisector of AB --> AP=PB, A(2,3) and B(3,2). X axis is bisector of BC means BX=XC, BX=2, XC=-2 --> C(3,-2) (D)
Attachments

PS202.png [ 10.08 KiB | Viewed 6013 times ]

_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Kudos [?]: 459 [0], given: 200

Manager
Joined: 29 Jul 2015
Posts: 159

Kudos [?]: 183 [0], given: 59

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

### Show Tags

28 Sep 2015, 04:45
Bunuel wrote:

In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). 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)

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 (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

The same way, since the x-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 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

The question becomes much easier if you just draw a rough sketch:
Attachment:
Reflection2.png
Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

Hope it helps.

Hi Bunuel
I solved this question with slope intercept form and took more than 2 minutes.
Can you please explain how did you conclude mirror reflection thing.
It would be really helpful if you could provide theory or link to theory which explains the concept of points and their mirror reflection with respect to lines, axes and quadrants.
Thanks

Kudos [?]: 183 [0], given: 59

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7671

Kudos [?]: 17339 [2], given: 232

Location: Pune, India
Re: In the rectangular coordinate system above, the line y = x [#permalink]

### Show Tags

28 Sep 2015, 21:01
2
KUDOS
Expert's post
kunal555 wrote:
Bunuel wrote:

In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). 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)

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 (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

The same way, since the x-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 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

The question becomes much easier if you just draw a rough sketch:
Attachment:
Reflection2.png
Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

Hope it helps.

Hi Bunuel
I solved this question with slope intercept form and took more than 2 minutes.
Can you please explain how did you conclude mirror reflection thing.
It would be really helpful if you could provide theory or link to theory which explains the concept of points and their mirror reflection with respect to lines, axes and quadrants.
Thanks

Here are 3 posts which explain this concept:
http://www.veritasprep.com/blog/2013/04 ... ry-part-i/
http://www.veritasprep.com/blog/2013/04 ... y-part-ii/
http://www.veritasprep.com/blog/2013/05 ... -part-iii/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 17339 [2], given: 232

Current Student
Joined: 12 Aug 2015
Posts: 301

Kudos [?]: 544 [0], given: 1474

Concentration: General Management, Operations
GMAT 1: 640 Q40 V37
GMAT 2: 650 Q43 V36
GMAT 3: 600 Q47 V27
GPA: 3.3
WE: Management Consulting (Consulting)
Re: In the rectangular coordinate system above, the line y = x [#permalink]

### Show Tags

25 May 2016, 05:14
after a bit of sketching you can easily reason out the solution. u understand that C lies in quadrant IV hence its coordinates are positive x and negative y. You kick A and B and then you kick out E. Between C and D: point C lies a bit further than point A hence they cannot share the same x coordinate. Then C out.
_________________

KUDO me plenty

Kudos [?]: 544 [0], given: 1474

Intern
Joined: 08 May 2016
Posts: 32

Kudos [?]: 8 [0], given: 24

Location: United States
WE: Project Management (Aerospace and Defense)
Re: In the rectangular coordinate system above, the line y = x [#permalink]

### Show Tags

21 Nov 2016, 12:11
Bunuel wrote:

In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). 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)

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 (3, 2). In any mirror reflection around the line y = x, the x-coordinate and the y-coordinate of a point become interchanged.

The same way, since the x-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 3, -2). In any mirror reflection around the x-axis, the x-coordinate remains the same, and the sign of the y-coordinate changes.

The question becomes much easier if you just draw a rough sketch:
Attachment:
Reflection2.png
Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
in-the-rectangular-coordinate-system-above-the-line-y-x-129932.html

Hope it helps.

Bunuel, thanks for such an elegant solution
_________________

Kudos [?]: 8 [0], given: 24

Re: In the rectangular coordinate system above, the line y = x   [#permalink] 21 Nov 2016, 12:11
Display posts from previous: Sort by