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# Math: Coordinate Geometry

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Math Expert
Joined: 02 Sep 2009
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09 Feb 2013, 02:11
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Archit143 wrote:
So for a question where it is given that slope is -1/6, Than how can be sure that line intersects 2nd quad, I found this question on GMAT prep......
in-the-rectangular-coordinate-system-shown-above-does-the-90635.html

Archit

As discussed, line with negative slope (-1/6<0) MUST intersect quadrants II and IV.
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09 Feb 2013, 03:45
HI Bunuel,
As karishma has also mentioned that a line with -ve slope can also be present in 1st quadrant than how can we be so sure that it is intersecting in 2nd quadrant,

Moreover as per the theory it must intersect in 2nd and 4th quadrant ...than as per statement 1 there are two possibilities.....line intersecting in in quad 2 and 4.....But we must have only one answer form the statement, for it to be correct answer..................

Archit
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09 Feb 2013, 03:53
Archit143 wrote:
HI Bunuel,
As karishma has also mentioned that a line with -ve slope can also be present in 1st quadrant than how can we be so sure that it is intersecting in 2nd quadrant,

Moreover as per the theory it must intersect in 2nd and 4th quadrant ...than as per statement 1 there are two possibilities.....line intersecting in in quad 2 and 4.....But we must have only one answer form the statement, for it to be correct answer..................

Archit

No, that's not what she said.

If the slope of a line is negative, line WILL intersect quadrants II and IV in ANY case. If X and Y intersects are positives, line ALSO intersects the quadrant I, if negative line ALSO intersects the quadrant quadrant III.
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09 Feb 2013, 22:53
Archit143 wrote:
So for a question where it is given that slope is -1/6, Than how can be sure that line intersects 2nd quad, I found this question on GMAT prep......
in-the-rectangular-coordinate-system-shown-above-does-the-90635.html

Archit

Since the slope is negative, the line will intersect the 2nd and 4th quadrant. We are talking about a line, not a line segment. A line extends indefinitely on both ends. The top end of the line will extend to intersect the 2nd quadrant under all circumstances.

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Karishma
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews VP Status: Final Lap Up!!! Affiliations: NYK Line Joined: 21 Sep 2012 Posts: 1072 Location: India GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31 GPA: 3.84 WE: Engineering (Transportation) Re: Math: Coordinate Geometry [#permalink] ### Show Tags 10 Feb 2013, 04:16 Karishma, thats what i wanted to ask....In question it asks about whether the line is intersecting 2nd quadrant....Answer is Yes it does, but at the same time it may lie in 1st quadrant also as explained by you....I think i am badly confused on this.... Archit Math Expert Joined: 02 Sep 2009 Posts: 43851 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 10 Feb 2013, 04:23 Archit143 wrote: Karishma, thats what i wanted to ask....In question it asks about whether the line is intersecting 2nd quadrant....Answer is Yes it does, but at the same time it may lie in 1st quadrant also as explained by you....I think i am badly confused on this.... Archit Does it matter whether the line also lies in other quadrants? We know that it goes through the II and IV quadrants, it may also (simultaneously) go through either I or III quadrant, but this does not alter the fact that the line goes through the II, is it? So, the answer is YES. _________________ VP Status: Final Lap Up!!! Affiliations: NYK Line Joined: 21 Sep 2012 Posts: 1072 Location: India GMAT 1: 410 Q35 V11 GMAT 2: 530 Q44 V20 GMAT 3: 630 Q45 V31 GPA: 3.84 WE: Engineering (Transportation) Re: Math: Coordinate Geometry [#permalink] ### Show Tags 10 Feb 2013, 06:27 Thanks Bunuel.... I got it.. Archit Manager Joined: 07 May 2012 Posts: 73 Location: United States Re: Math: Coordinate Geometry [#permalink] ### Show Tags 06 Apr 2013, 08:06 Hi Bunuel, Thanks for the consolidated , yet elaborate content for the topic at one place. I would be glad , if you can tell me as to , how did you arrive at the formula for the vertex of a parabola. I find it difficult to remember formulas and if there is a easy way to arrive at the formula itself , then would prefer to know that too , so it helps in case I forget the formula. Appreciate any help on this. Thanks, Jyothi _________________ Jyothi hosamani Math Expert Joined: 02 Sep 2009 Posts: 43851 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 10 Jul 2013, 23:06 Bumping for review*. *New project from GMAT Club!!! Check HERE _________________ Intern Joined: 24 Apr 2013 Posts: 5 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 05 Aug 2013, 10:19 Hi bunuel, firstly i want to thank for the explanations you provide to questions because most of them are pretty conceptual and healthy to understand. Secondly, i wished i was more thorough with my concepts in co-ordinate geometry specifically PARABOLA. i had seen two parabola questions when i took the test & both were quite hard unfortunately, had to end up guessing. Have yu posted any questions related to Parabola ?? Non-Human User Joined: 09 Sep 2013 Posts: 13814 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 08 Aug 2014, 21:38 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. _________________ Intern Joined: 23 Aug 2014 Posts: 42 GMAT Date: 11-29-2014 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 25 Nov 2014, 23:21 1 This post was BOOKMARKED The angle of inclination of a line with slope 1 is 45 degrees. I know that the angle for a line of slope 2 is not 90 degree, but i do not know why not. Please help Intern Joined: 15 Dec 2014 Posts: 1 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 04 May 2015, 11:45 All of the formulas in this post using division are messed up. I believe the formatting or something has changed and caused this error. Please fix this! See the current formula for the slop as an example. Math Expert Joined: 02 Sep 2009 Posts: 43851 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 04 May 2015, 23:52 Jamie19892000 wrote: All of the formulas in this post using division are messed up. I believe the formatting or something has changed and caused this error. Please fix this! See the current formula for the slop as an example. Everything looks fine for me. Can you please post a screenshot? _________________ Non-Human User Joined: 09 Sep 2013 Posts: 13814 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 05 May 2016, 02:23 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. _________________ Intern Joined: 29 Nov 2015 Posts: 7 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 10 May 2016, 20:47 Thanks Bunuel this is my weak subject for the gmat. Posted from my mobile device Intern Joined: 12 Dec 2016 Posts: 12 Re: Math: Coordinate Geometry [#permalink] ### Show Tags 22 Mar 2017, 12:14 Can you please explain here; To answer, we must find the slope of each line and then check to see if one slope is the negative reciprocal of the other or if their product equals to -1. SlopeAB=5−199−48=−14−39=0.358SlopeAB=5−199−48=−14−39=0.358 SlopeCD=24−422−31=20−9=−2.22 The formula of the slope of two given coordinates are y2-y1 / x2-x1 However in some questions, 2nd coordinates (x2 y2)s are subtracted from 1sts (x1 y1) and in some, other way around. Can you please clarify what do we take into account concerning this formula? Board of Directors Status: Aiming MBA Joined: 18 Jul 2015 Posts: 3074 Location: India Concentration: Healthcare, Technology GPA: 3.65 WE: Information Technology (Health Care) Re: Math: Coordinate Geometry [#permalink] ### Show Tags 22 Mar 2017, 22:52 1 This post received KUDOS mesutthefail wrote: Can you please explain here; To answer, we must find the slope of each line and then check to see if one slope is the negative reciprocal of the other or if their product equals to -1. SlopeAB=5−199−48=−14−39=0.358SlopeAB=5−199−48=−14−39=0.358 SlopeCD=24−422−31=20−9=−2.22 The formula of the slope of two given coordinates are y2-y1 / x2-x1 However in some questions, 2nd coordinates (x2 y2)s are subtracted from 1sts (x1 y1) and in some, other way around. Can you please clarify what do we take into account concerning this formula? Hi, This is a mathematical rule. You can write a-b = -(b-a). Did you get this rule?? Now, in a similar way if you take - sign common from both numerator and denominator of y2-y1 / x2-x1, you will get -(y1-y2)/-(x1-x2). I hope you are aware of the rule that - signs can be cancelled out both a numerator and denominator. So, we will be left with the formula, Slope = (y1-y2)/(x1-x2). I hope that makes sense. _________________ How I improved from V21 to V40! ? How to use this forum in THE BEST way? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7944 Location: Pune, India Re: Math: Coordinate Geometry [#permalink] ### Show Tags 23 Mar 2017, 03:22 mesutthefail wrote: Can you please explain here; To answer, we must find the slope of each line and then check to see if one slope is the negative reciprocal of the other or if their product equals to -1. SlopeAB=5−199−48=−14−39=0.358SlopeAB=5−199−48=−14−39=0.358 SlopeCD=24−422−31=20−9=−2.22 The formula of the slope of two given coordinates are y2-y1 / x2-x1 However in some questions, 2nd coordinates (x2 y2)s are subtracted from 1sts (x1 y1) and in some, other way around. Can you please clarify what do we take into account concerning this formula? They are both the same. $$Slope = \frac{(y2 - y1)}{(x2 - x1)} = \frac{(y1 - y2)}{(x1 - x2)}$$ Take an example: (x1, y1) = (2, 3) (x2, y2) = (5, -10) $$Slope = \frac{(y2 - y1)}{(x2 - x1)} = \frac{-10 - 3}{5 - 2} = -\frac{13}{3}$$ $$Slope = \frac{(y1 - y2)}{(x1 - x2)} = \frac{3- (-10)}{2 - 5} = -\frac{13}{3}$$ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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01 Sep 2017, 23:22
Hello Bunuel,

Thanks a lot for the article. I have one doubt . Is it that a line with negative slope would definitely pass through Quadrant 2 and 4, and would pass through 1 or 3 depending on the value of x and y intersects?
Re: Math: Coordinate Geometry   [#permalink] 01 Sep 2017, 23:22

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