GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Feb 2019, 07:05

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• ### Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT

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

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 467
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

31 Mar 2012, 01:54
3
39
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:43) correct 27% (02:15) wrong based on 826 sessions

### HideShow timer Statistics

Attachment:

Capture.GIF [ 3.28 KiB | Viewed 33707 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 (1, 4), what are the coordinates of point C?

A. (-4, -1)
B. (-1, 4)
C. (4, -1)
D. (1, -4)
E. (4, 1)

_________________

Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730

Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

31 Mar 2012, 03:26
14
21
enigma123 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 (1, 4), what are the coordinates of point C?

A. (-4, -1)
B. (-1, 4)
C. (4, -1)
D. (1, -4)
E. (4, 1)

Since the line y=x is the perpendicular bisector of segment AB, then the point B is the mirror reflection of point A around the line y=x, so its coordinates are (4, 1). 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 x-axis, so its coordinates are (4, -1).

The question becomes much easier if you just draw rough sketch of the diagram:
Attachment:

graph.png [ 12.57 KiB | Viewed 33692 times ]
Now, you can simply see that options A, B, and D (blue dots) just can not be the right answers. As for option E: point (4, 1) coincides with point B, so it's also not the correct answer. Only answer choice C remains.

Similar questions to practice:
in-the-xy-coordinate-plane-is-point-r-equidistant-from-143502.html
in-the-rectangular-coordinate-system-the-line-y-x-is-the-132646.html
the-coordinates-of-points-a-and-c-are-0-3-and-127769.html
the-line-represented-by-the-equation-y-4-2x-is-the-127770.html
if-point-a-coordinates-are-7-3-point-b-coordinates-a-141972.html
in-the-rectangular-coordinate-system-the-line-y-x-is-the-88473.html
in-the-rectangular-coordinate-system-above-the-line-y-x-144774.html
the-line-represented-by-the-equation-y-4-2x-is-the-perpendi-87573.html

Hope it helps.
_________________
Director
Joined: 22 Mar 2011
Posts: 599
WE: Science (Education)
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

01 Aug 2012, 05:56
3
4
teal wrote:
What is the mirror image of a point (x,y) around Y-axis?
Also what is the mirror image of a point (x,y) around line y=-x?

The mirror image of $$(x,y)$$ around the Y-axis is $$(-x,y)$$.

For the second question:
Assume we have a point P(a,b) and we want to find its mirror image around the line $$y = -x$$.
Let's denote the point we seek by Q(A,B). See the attached drawing.

The equation of the line passing through P and perpendicular to the line $$y = -x$$ is $$y - b = x - a$$, or $$y = x + b - a$$.
Since Q is also on this line, we have $$B = A + b - a$$, from which $$A - B = a - b$$.
The middle point of the line segment PQ (denoted by M) is also on the line $$y = -x$$, therefore $$\frac{a+A}{2}=-\frac{b+B}{2}$$, or $$A + B = -a - b$$.
Solving for A and B, we find that $$A = -b, B =-a$$.

Therefore, the mirror image of $$(x,y)$$ around the line $$y = -x$$ is $$(-y, -x)$$.
Attachments

MirrorImage.jpg [ 18.1 KiB | Viewed 32945 times ]

_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

##### General Discussion
Manager
Joined: 13 May 2010
Posts: 110
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

01 Aug 2012, 04:04
1
What is the mirror image of a point (x,y) around Y-axis?

Also what is the mirror image of a point (x,y) around line y=-x?
Senior Manager
Joined: 13 Aug 2012
Posts: 420
Concentration: Marketing, Finance
GPA: 3.23
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

02 Jan 2013, 04:09
1
enigma123 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 (1, 4), what are the coordinates of point C?

A. (-4, -1)
B. (-1, 4)
C. (4, -1)
D. (1, -4)
E. (4, 1)

Any idea guys how to solve this mathematically?

For me, the best approach to this question is to draw and estimate AB and BC lines. Doing so obviously shows that:
(a) y has negative coordinates... Thus, eliminate B and E.
(b) x has positive coordinates beyond 2. Thus, eliminate A and D.

Or, if you want to be really sure... We can get the line perpendicular x=y.
(a) get negative reciprocal of slope of y=x which is m=1. Thus, reciprocal is m=-1. Perpendicular line: y=-x + b
(b) calculate b using A coordinates: y = -x + b ==> 4 = -1 + b ==> b = 5
(c) get the pt. of intersection. -x + 5 = x ==> x = 2.5
(d) get y=-(2.5) + 5 --> y = 2.5

So, obviously... C would have negative for y coordinate and x > 2.5... only C fits the bill

But still, drawing should suffice...
_________________

Impossible is nothing to God.

Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

27 Jun 2013, 22:47
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
All PS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=62

_________________
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

27 Jun 2013, 23:31
2
3
enigma123 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 (1, 4), what are the coordinates of point C?

A. (-4, -1)
B. (-1, 4)
C. (4, -1)
D. (1, -4)
E. (4, 1)

Let the co-ordinates of B = (p,q). As x=y is the perpendicular bisector of the line segment AB, thus the middle point of AB will lie on x=y itself. Thus, for A(1,4) and B(p,q)-->

$$\frac {p+1} {2} = \frac {q+4} {2}$$ --> p-q = 3

Also, the slope of the line segment would be -1--> $$\frac {q-4}{p-1} = -1$$ --> $$p+q = 5$$.Thus, on solving, the co-ordinates of B (4,1).

Similarly, as y=0(the x-axis) is the perpendicular bisector of BC, thus, the mid point of BC would like on the x-axis and thus, the y co-ordinate of C has to be -1. Thus, only A and C survive. Again, the slope of line segment BC has to be undefined as it is parallel to the y-axis(or perpendicular to the x axis).

Only option C survives.

C.
_________________
MBA Section Director
Affiliations: GMAT Club
Joined: 21 Feb 2012
Posts: 6056
City: Pune
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

28 Jun 2013, 04:36
2
Bunuel wrote:
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

The line Y = X always makes 45 deg angle with the X axis and has slope 1

Since the line Y = X is perpendicular to line AB, The slope of AB must be -1 --------[The product of the slopes of a line and its perpendicular is always -1]

Hereinafter, Even if we are not familiar with 'mirror image' concept we can draft the following figure and can check the answer options.

Since X axis itself is bisector of line BC we can deduce that X value of C can not be negative. Eliminate A, B

We also know Y value of C can not be positive. Eliminate E

Now consider the point A(1,4) This point is on the line that has slope -1, so the X value of its opposite end (i.e. X of B and C also) must be greater than 1. So Choice D (1, -4) Can not be the location of C. Eliminate.

Only option left is C, which is the Answer.
_________________

Starts from Feb 4th: MBA Video Series, Video answers to specific components and questions about the MBA application.

Intern
Joined: 24 Jun 2014
Posts: 38
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

29 Nov 2014, 20:36
EvaJager wrote:
teal wrote:
What is the mirror image of a point (x,y) around Y-axis?
Also what is the mirror image of a point (x,y) around line y=-x?

The mirror image of $$(x,y)$$ around the Y-axis is $$(-x,y)$$.

For the second question:
Assume we have a point P(a,b) and we want to find its mirror image around the line $$y = -x$$.
Let's denote the point we seek by Q(A,B). See the attached drawing.

The equation of the line passing through P and perpendicular to the line $$y = -x$$ is $$y - b = x - a$$, or $$y = x + b - a$$.
Since Q is also on this line, we have $$B = A + b - a$$, from which $$A - B = a - b$$.
The middle point of the line segment PQ (denoted by M) is also on the line $$y = -x$$, therefore $$\frac{a+A}{2}=-\frac{b+B}{2}$$, or $$A + B = -a - b$$.
Solving for A and B, we find that $$A = -b, B =-a$$.

Therefore, the mirror image of $$(x,y)$$ around the line $$y = -x$$ is $$(-y, -x)$$.

Hi I have one question. What if the question ask to find the mirror image of (x,y) around the line y = 2x + 3 for example, how to solve it?
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4972
Location: United States (CA)
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

13 Jul 2016, 06:37
1
enigma123 wrote:
Attachment:
Capture.GIF
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 (1, 4), what are the coordinates of point C?

A. (-4, -1)
B. (-1, 4)
C. (4, -1)
D. (1, -4)
E. (4, 1)

This problem does contain a diagram that looks like the following:

We are given that the line y = x is a perpendicular bisector of line segment AB. This indicates that point B is a reflection of point A across the line y = x. When we reflect a point (a,b) across the line y = x, the reflected point has the coordinates reversed: (b,a). Thus, since point A is at (2,3), point B must be (3,2).

We are next given that the x-axis is a perpendicular bisector of line segment BC. This means that point C must have the same x-coordinate as point B (3) but the opposite y-coordinate of point B (-2). To further elaborate, we can draw a diagram.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Joined: 06 Oct 2015
Posts: 91
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

22 Oct 2016, 05:06
Hi Bunuel,
Is it always true that a perpendicular bisector will have mirror reflection of the ends?
Board of Directors
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3631
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

22 Oct 2016, 05:26
NaeemHasan wrote:
Hi Bunuel,
Is it always true that a perpendicular bisector will have mirror reflection of the ends?

Yes, it is always true.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.
New! Best Reply Functionality on GMAT Club!
Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free
Check our new About Us Page here.

Intern
Joined: 07 Dec 2016
Posts: 40
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

07 Sep 2017, 09:40
I took the approach of eliminating the options.

Since X-axis is perpendicular bisector of line BC, it means that B will line in I quadrant and C in IV quadrant . This means for point C x-cordinate will be +ve and y-co-ordinate will be negative. With this finding , remove options A,B and E

Now as per option D if point C is (1,-4) then point B will be (1,+4). But (1,4) is co-ordinate of point A.

Non-Human User
Joined: 09 Sep 2013
Posts: 9892
Re: In the rectangular coordinate system above, the line y = x  [#permalink]

### Show Tags

05 Oct 2018, 21:30
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 above, the line y = x   [#permalink] 05 Oct 2018, 21:30
Display posts from previous: Sort by