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## Coordinate Geo

tagged by: Brent@GMATPrepNow

This topic has 4 expert replies and 3 member replies
akhilsuhag Really wants to Beat The GMAT!
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Coordinate Geo 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

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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

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knight247 GMAT Destroyer!
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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

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Brent@GMATPrepNow GMAT Instructor
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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

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Brent@GMATPrepNow GMAT Instructor
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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

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Brent Hanneson - GMAT Prep Now instructor
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knight247 GMAT Destroyer!
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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

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Brent@GMATPrepNow GMAT Instructor
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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

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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
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- Our top 3 free videos:
1) The Double Matrix method
3) Managing your time on the GMAT

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Brent@GMATPrepNow GMAT Instructor
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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
- Watch hours of free videos on DS, RC and AWA
- Our top 3 free videos:
1) The Double Matrix method
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.

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