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. February 23, 2019 February 23, 2019 07:00 AM PST 09:00 AM PST Learn reading strategies that can help even nonvoracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
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
Concentration: International Business, Strategy
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
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 xaxis 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)
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
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
enigma123 wrote: In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the xaxis 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 xaxis is the perpendicular bisector of segment BC then the point C is the mirror reflection of point B around the xaxis, so its coordinates are (4, 1). Answer: C. 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. Answer: C. Similar questions to practice: inthexycoordinateplaneispointrequidistantfrom143502.htmlintherectangularcoordinatesystemthelineyxisthe132646.htmlthecoordinatesofpointsaandcare03and127769.htmlthelinerepresentedbytheequationy42xisthe127770.htmlifpointacoordinatesare73pointbcoordinatesa141972.htmlintherectangularcoordinatesystemthelineyxisthe88473.htmlintherectangularcoordinatesystemabovethelineyx144774.htmlthelinerepresentedbytheequationy42xistheperpendi87573.htmlHope it helps.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




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
teal wrote: What is the mirror image of a point (x,y) around Yaxis? Also what is the mirror image of a point (x,y) around line y=x? The mirror image of \((x,y)\) around the Yaxis 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.




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
What is the mirror image of a point (x,y) around Yaxis?
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
enigma123 wrote: In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the xaxis 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.
Answer: C 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 Answer: C 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



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
enigma123 wrote: In the rectangular coordinate system above, the line y = x is the perpendicular bisector of segment AB (not shown), and the xaxis 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 coordinates 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)> \(\frac {p+1} {2} = \frac {q+4} {2}\) > pq = 3 Also, the slope of the line segment would be 1> \(\frac {q4}{p1} = 1\) > \(p+q = 5\).Thus, on solving, the coordinates of B (4,1). Similarly, as y=0(the xaxis) is the perpendicular bisector of BC, thus, the mid point of BC would like on the xaxis and thus, the y coordinate 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 yaxis(or perpendicular to the x axis). Only option C survives. C.
_________________
All that is equal and notDeep Dive Inequality
Hit and Trial for Integral Solutions



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
Bunuel wrote: Bumping for review and further discussion*. Get a kudos point for an alternative solution! *New project from GMAT Club!!! Check HEREThe 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 Yaxis? Also what is the mirror image of a point (x,y) around line y=x? The mirror image of \((x,y)\) around the Yaxis 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
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 xaxis 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 xaxis is a perpendicular bisector of line segment BC. This means that point C must have the same xcoordinate as point B (3) but the opposite ycoordinate of point B (2). To further elaborate, we can draw a diagram. The answer is D.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Joined: 06 Oct 2015
Posts: 91
Location: Bangladesh
Concentration: Accounting, Leadership

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 Blog: Subscribe to Question of the Day Blog 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
Concentration: Strategy, International Business

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 Xaxis 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 xcordinate will be +ve and ycoordinate 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 coordinate of point A.
So,correct answer is C.



NonHuman 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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: In the rectangular coordinate system above, the line y = x
[#permalink]
05 Oct 2018, 21:30






