GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Jul 2020, 15:24 ### 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.  # In the rectangular coordinate system above, the line y = x

Author Message
TAGS:

### Hide Tags

Manager  Joined: 02 Dec 2012
Posts: 172
In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

16
79 00:00

Difficulty:   45% (medium)

Question Stats: 72% (02:04) correct 28% (02:22) wrong based on 1474 sessions

### HideShow timer Statistics 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)

Attachment: Reflcetion.png [ 8.39 KiB | Viewed 21450 times ]
Math Expert V
Joined: 02 Sep 2009
Posts: 65062
In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

15
33 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: Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
http://gmatclub.com/forum/in-the-rectan ... 32646.html
http://gmatclub.com/forum/in-the-rectan ... 29932.html

Hope it helps.

Attachment: Reflection2.png [ 10.75 KiB | Viewed 20643 times ]

_________________
Intern  Joined: 04 Aug 2013
Posts: 5
Concentration: Sustainability, Entrepreneurship
WE: Architecture (Energy and Utilities)
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

5
2
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.
##### General Discussion
Intern  Joined: 15 Feb 2015
Posts: 13
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

For this question, I am confused. where do I get the position of B and C?
Thanks ...
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

2
6
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

Current Student B
Joined: 10 Mar 2013
Posts: 448
Location: Germany
Concentration: Finance, Entrepreneurship
Schools: WHU MBA"20 (A\$)
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

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 15030 times ]

Manager  Joined: 29 Jul 2015
Posts: 150
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

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
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

2
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

Senior Manager  Joined: 12 Aug 2015
Posts: 277
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

1
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.
SVP  V
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1676
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

1
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: Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
http://gmatclub.com/forum/in-the-rectan ... 32646.html
http://gmatclub.com/forum/in-the-rectan ... 29932.html

Hope it helps.

Bunuel, why we didn't extend line AB more to have some other co-ordinates for B? Say, if AB cuts line xy at point P perpendicularly, then is it necessary that AP = PB?
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Math Expert V
Joined: 02 Sep 2009
Posts: 65062
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

QZ 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: Now, you can simply see that only D can be the correct answer.

Similar questions to practice:
http://gmatclub.com/forum/in-the-rectan ... 32646.html
http://gmatclub.com/forum/in-the-rectan ... 29932.html

Hope it helps.

Bunuel, why we didn't extend line AB more to have some other co-ordinates for B? Say, if AB cuts line xy at point P perpendicularly, then is it necessary that AP = PB?

A perpendicular bisector is a line which cuts a line segment into two equal parts at 90°.

So, if you extend AB, y = x will no longer be a bisector of segment AB.
_________________
Manager  S
Status: Don't Give Up!
Joined: 15 Aug 2014
Posts: 97
Location: India
Concentration: Operations, General Management
GMAT Date: 04-25-2015
WE: Engineering (Manufacturing)
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

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)

Hi, i could not understand adding up 0.5 part. Can you please explain in detail?

Posted from my mobile device
IIMA, IIMC School Moderator V
Joined: 04 Sep 2016
Posts: 1427
Location: India
WE: Engineering (Other)
In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

For this blog, could you explain how did you deduce a 30-60-90 triangle from only knowing that radius of circle / hypotenuse = 2? The length of minute clock is fixed, so if I join center to number 9 and center to number 12, both lengths of both these segments will be the same. Right?
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10646
Location: Pune, India
In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

2

For this blog, could you explain how did you deduce a 30-60-90 triangle from only knowing that radius of circle / hypotenuse = 2? The length of minute clock is fixed, so if I join center to number 9 and center to number 12, both lengths of both these segments will be the same. Right?

When the minute hand is at 9 to when it goes to 12, it sweeps a 90 degree angle. This means that from 9 to 10, it sweeps 30 degrees, from 10 to 11, it sweeps another 30 degrees and from 11 to 12, it sweeps yet another 30 degrees - making a total of 90 degrees.
Hence, from 9 to 10, the angle would be 30 degrees, making the shown triangles 30-60-90. Since hypotenuse is 2, the other two sides must be 1 and sqrt(3).
_________________
Karishma
Veritas Prep GMAT Instructor

Intern  B
Joined: 23 Sep 2019
Posts: 6
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

One of these problems where looking at the answer choices before tackling the problem is really helpful and efficient.

Posted from my mobile device Re: In the rectangular coordinate system above, the line y = x   [#permalink] 25 May 2020, 14:17

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