Welcome! Check out our free B-School Guides to learn how you compare with other applicants.
Login or Register
 

Coordinate Geo

This topic has 4 expert replies and 3 member replies
Bookmark
Previous Topic Next Topic
akhilsuhag Really wants to Beat The GMAT!
Joined
04 Jul 2011
Posted:
261 messages
Followed by:
3 members
Thanked:
45 times
Target GMAT Score:
720+
Coordinate Geo Post Sun Sep 04, 2011 4:09 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    A line with the equation y = px + q is reflected over the line y = x. Is the reflection of this line parallel to the line y = mx + n?

    (1) m = p + 2

    (2) m = 3p

    OA: C

    _________________
    Please press "thanks" if you think my post has helped you.. Cheers!!

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    cans GMAT Titan
    Joined
    04 Apr 2011
    Posted:
    1308 messages
    Followed by:
    111 members
    Thanked:
    297 times
    Test Date:
    13th Oct
    Target GMAT Score:
    750+
    GMAT Score:
    750
    Post Mon Sep 05, 2011 5:44 am
    y=px+q. Line reflected on y=x will have slope 1/p.
    Thus m=1/p means true.
    p+2 = 1/p -> possible also and not possible also.
    3p = 1/p -> insufficient.
    both combined -> p=1. Thus parallel.
    Sufficient
    IMO C

    _________________
    If my post helped you- let me know by pushing the thanks button Wink

    Cans!!

    knight247 GMAT Destroyer!
    Joined
    19 Apr 2011
    Posted:
    477 messages
    Followed by:
    11 members
    Thanked:
    113 times
    Target GMAT Score:
    800
    Post Mon Sep 05, 2011 7:25 am
    Just a clarification that I need. For line y=px+q the slope is p and its reflection will be in the same plane so even the reflection will have a slope of p rite? Also for y = mx + n the slope is m. So if they are both parallel then m=p. Which is what we need to prove. Now, if statement 1 tells u that that m-p=2 then m and p are different. So if their slopes are different then how could they be parallel? Similarly with statement 2? Don't know if I'm asking the right question. Or maybe there is some property of a reflected line that I have not understood. Hoping someone can clarify that for me.
    Thanks

    GMAT/MBA Expert

    Brent@GMATPrepNow GMAT Instructor
    Joined
    08 Dec 2008
    Posted:
    3920 messages
    Followed by:
    607 members
    Thanked:
    1701 times
    GMAT Score:
    770
    Most Active Expert Most Responsive Expert Most Thanked Expert
    Post Mon Sep 05, 2011 8:05 am
    knight247 wrote:
    Just a clarification that I need. For line y=px+q the slope is p and its reflection will be in the same plane so even the reflection will have a slope of p rite?
    If we take the line y = px+q and reflect it over the line y=x, the reflected line will have slope 1/p

    Having said that, I'm pretty sure that this question is out-of-scope. I've never seen an official GMAT question that requires one to know that the reflected line (across the line y=x) will have slope 1/p, and I've never seen this concept mentioned in the GMAT curriculum.

    Aside: I'm sure that there are people who remember this concept from high school, and for those people the question will not be a big deal. But, if we're interested in answering the question "Is the concept of reflecting lines across the line y=x within the scope of the GMAT?", my answer is no.

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Thanked by: knight247
    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.

    GMAT/MBA Expert

    Brent@GMATPrepNow GMAT Instructor
    Joined
    08 Dec 2008
    Posted:
    3920 messages
    Followed by:
    607 members
    Thanked:
    1701 times
    GMAT Score:
    770
    Most Active Expert Most Responsive Expert Most Thanked Expert
    Post Mon Sep 05, 2011 8:10 am
    I should add that I think it is within the scope of the GMAT to ask questions where we reflect individual points across the line y=x. (I just think that reflecting lines is out-of-scope)

    In general, if the point (x,y) is reflected across the line y=x, the reflected point is at (y,x)
    So, for example, if the point (3,1) is reflected across the line y=x, the reflected point is at (3,1).

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Thanked by: akhilsuhag
    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.
    knight247 GMAT Destroyer!
    Joined
    19 Apr 2011
    Posted:
    477 messages
    Followed by:
    11 members
    Thanked:
    113 times
    Target GMAT Score:
    800
    Post Tue Sep 06, 2011 12:40 am
    Hey Brent,
    Appreciate ur response. Is there any way that you could help prove that the slope of line y=mx+b reflected over y=x is 1/m? I'm having a hard time understanding how that is so. Or maybe if you could show me any links where I could learn that. Also, Are there any other similar properties or corollaries related to reflections over y=x that are important to know. I mean, besides the two mentioned here. Thanks

    GMAT/MBA Expert

    Brent@GMATPrepNow GMAT Instructor
    Joined
    08 Dec 2008
    Posted:
    3920 messages
    Followed by:
    607 members
    Thanked:
    1701 times
    GMAT Score:
    770
    Most Active Expert Most Responsive Expert Most Thanked Expert
    Post Tue Sep 06, 2011 7:35 am
    knight247 wrote:
    Hey Brent,
    Appreciate ur response. Is there any way that you could help prove that the slope of line y=mx+b reflected over y=x is 1/m? I'm having a hard time understanding how that is so. Or maybe if you could show me any links where I could learn that. Also, Are there any other similar properties or corollaries related to reflections over y=x that are important to know. I mean, besides the two mentioned here. Thanks
    Aside: This is pretty esoteric stuff. You certainly don't need to know this rule or this proof for the GMAT.

    That said, here's a pretty rudimentary proof:

    If the line y=mx+b is reflected across the line y=x, the equation of the reflected line is x=my+b (to find the equation of any reflected line across y=x, just switch the x's and y's)

    Now let's find 2 points on the reflected line x=my+b

    When y=0, we get x=m(0)+b, which equals b.
    So, one point on the line is (b,0)

    When y=1, we get x=m(1)+b, which equals m+b.
    So, a second point on the line is (m+b,1)

    When we use the slope formula to find the slope between these two points, we get:
    Slope = [1-0]/[(m+b)-(b)] = 1/m

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Thanked by: knight247
    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.

    GMAT/MBA Expert

    Brent@GMATPrepNow GMAT Instructor
    Joined
    08 Dec 2008
    Posted:
    3920 messages
    Followed by:
    607 members
    Thanked:
    1701 times
    GMAT Score:
    770
    Most Active Expert Most Responsive Expert Most Thanked Expert
    Post Tue Sep 06, 2011 7:38 am
    knight247 wrote:
    Are there any other similar properties or corollaries related to reflections over y=x that are important to know. I mean, besides the two mentioned here. Thanks
    Sorry, I forgot to address this question.

    For the GMAT, all you really need to know about reflections across the line y=x is that when the point (x,y) is reflected across the line y=x, the reflected point is at (y,x)

    Cheers,
    Brent

    _________________
    Brent Hanneson - GMAT Prep Now instructor
    - Check out GMAT Prep Now’s online course at http://www.gmatprepnow.com/
    - Use our video course in conjunction with Beat The GMAT's free 60-Day Study Guide
    - Watch hours of free videos on DS, RC and AWA
    - Our top 3 free videos:
    1) The Double Matrix method
    2) Calculating combinations in your head
    3) Managing your time on the GMAT

    Thanked by: knight247
    Study Smart! Use Beat The GMAT’s FREE 60-Day Study Guide in conjunction with GMAT Prep Now’s video course and reach your target score in 2 months! With two money-back guarantees, you can try us out risk-free.

    Best Conversation Starters
    1 varun289 31 topics
    2 sana.noor 23 topics
    3 killerdrummer 21 topics
    4 Rudy414 19 topics
    5 sanaa.rizwan 14 topics
    See More Top Beat The GMAT Members...

    Most Active Experts
    1 image description Brent@GMATPrepNow

    GMAT Prep Now Teacher

    		 199 posts
    2 image description GMATGuruNY

    The Princeton Review Teacher

    		 134 posts
    3 image description Jim@StratusPrep

    Stratus Prep

    		 106 posts
    4 image description Anju@Gurome

    Gurome

    		 47 posts
    5 image description Jon@Admissionado

    Admissionado

    		 39 posts
    See More Top Beat The GMAT Experts