Math: Coordinate Geometry : GMAT Quantitative Section - Page 2
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 24 Jan 2017, 11:17

### 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 June
Open Detailed Calendar

# Math: Coordinate Geometry

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 22 Dec 2009
Posts: 362
Followers: 11

Kudos [?]: 378 [2] , given: 47

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

21 Feb 2010, 03:00
2
KUDOS
2
This post was
BOOKMARKED
Bunuel wrote:
Slope of a Line

The slope or gradient of a line describes its steepness, incline, or grade. A higher slope value indicates a steeper incline.

The slope is defined as the ratio of the "rise" divided by the "run" between two points on a line, or in other words, the ratio of the altitude change to the horizontal distance between any two points on the line.

Given two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$ on a line, the slope $$m$$ of the line is:

$$m=\frac{y_2-y_1}{x_2-x_1}$$

If the equation of the line is given in the Point-intercept form: $$y=mx+b$$, then $$m$$ is the slope. This form of a line's equation is called the slope-intercept form, because $$b$$ can be interpreted as the y-intercept of the line, the y-coordinate where the line intersects the y-axis.

If the equation of the line is given in the General form:$$ax+by+c=0$$, then the slope is $$-\frac{a}{b}$$ and the y intercept is $$-\frac{c}{b}$$.

SLOPE DIRECTION
The slope of a line can be positive, negative, zero or undefined.

Positive slope
Here, y increases as x increases, so the line slopes upwards to the right. The slope will be a positive number. The line below has a slope of about +0.3, it goes up about 0.3 for every step of 1 along the x-axis.

Negative slope
Here, y decreases as x increases, so the line slopes downwards to the right. The slope will be a negative number. The line below has a slope of about -0.3, it goes down about 0.3 for every step of 1 along the x-axis.

Zero slope
Here, y does not change as x increases, so the line in exactly horizontal. The slope of any horizontal line is always zero. The line below goes neither up nor down as x increases, so its slope is zero.
Undefined slope
When the line is exactly vertical, it does not have a defined slope. The two x coordinates are the same, so the difference is zero. The slope calculation is then something like $$slope=\frac{15}{0}$$ When you divide anything by zero the result has no meaning. The line above is exactly vertical, so it has no defined slope.

1. If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin $$(0,0)$$ OR is parallel to either of axis crosses only two quadrants.

4. If a line is horizontal it has a slope of $$0$$, is parallel to X-axis and crosses quadrant I and II if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is $$x=a$$, where a is x-intercept.

6. For a line that crosses two points $$(x_1,y_1)$$ and $$(x_2,y_2)$$, slope $$m=\frac{y_2-y_1}{x_2-x_1}$$

7. If the slope is 1 the angle formed by the line is $$45$$ degrees.

8. Given a point and slope, equation of a line can be found. The equation of a straight line that passes through a point $$(x_1, y_1)$$ with a slope $$m$$ is: $$y - y_1 = m(x - x_1)$$

A general question on Slope....

I know the an absolute value of a slope gives us how steep the line would be. And the sign gives us whether it is a rise or a fall...

But if we have a question like:
Line A has a slope -5 and Line B has a slope 4.... Which one of them has a greater slope? How do we handle this? Does this mean we consider the absolute values and then decide or answer.. (that is Line A)... or should we consider the signs too.. (i.e. Line B)...

_________________

Cheers!
JT...........
If u like my post..... payback in Kudos!!

|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice|
|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93656 [0], given: 10583

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

21 Feb 2010, 07:55
jeeteshsingh wrote:
A general question on Slope....

I know the an absolute value of a slope gives us how steep the line would be. And the sign gives us whether it is a rise or a fall...

But if we have a question like:
Line A has a slope -5 and Line B has a slope 4.... Which one of them has a greater slope? How do we handle this? Does this mean we consider the absolute values and then decide or answer.. (that is Line A)... or should we consider the signs too.. (i.e. Line B)...

If the question is which one has the greater slope, then the answer would be: Line B, as 4>-5. As you correctly noted line A will be steeper than B, but the slope of B is positive and that of A is negative. We are comparing m1 with m2 not |m1| with |m2|.
_________________
Senior Manager
Joined: 13 Dec 2009
Posts: 263
Followers: 10

Kudos [?]: 184 [7] , given: 13

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

09 May 2010, 10:30
7
KUDOS
3
This post was
BOOKMARKED
There's one formula I'd like to add to the list:

Area of a triangle given the three vertices of the triangle ($$x1, y1$$), ($$x2, y2$$) and ($$x3, y3$$)

$$A = \frac{1}{2} * [x1(y2-y3) + x2(y3-y1) + x3(y1-y2)]$$

To remember the order of variables just remember 1,2,3 then 2,3,1 and 3,1,2.

This would be useful in coordinate geometry in case the triangle does not rest on one of the axes and you know the three vertices.
_________________

My debrief: done-and-dusted-730-q49-v40

Manager
Joined: 06 Mar 2010
Posts: 107
Followers: 2

Kudos [?]: 5 [0], given: 11

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

27 Jun 2010, 11:09
Great post, cleared the basics of the co-ordinate geometry.
Manager
Joined: 23 Oct 2009
Posts: 84
Location: New Delhi, India
Schools: Chicago Booth, Harvard, LBS, INSEAD, Columbia
Followers: 7

Kudos [?]: 16 [0], given: 76

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

05 Jul 2010, 06:47
Thank you so much for this chapter! It's very well written.
One suggestion though - when we're actually doing GMAT question, and there is a fraction involved in the calculation, it is more often than not better to avoid converting it into decimal form until the absolute end of the question. Two reasons:
1. In Example #1 under Parellel lines section, it is not necessary to convert the slopes 14/29 and 20/-9 into decimal form. This is because the question requires us to figure out if the slopes are equal or not, and from the fraction form itself we can figure that out.
2. Often, you will be able to cancel out some parts of your fraction in a calculation that is to take place in the next step. For example, 9/2 is x. Find 2x. Answer: 9. (too easy example, but i hope u get the point.)
_________________

Read about my GMAT prep at http://gmatting.blogspot.com/
1st Feb '11 -- Actual GMAT : 730 (Q48 V42) AWA 6.0

My Practice GMAT Scores
29th Jan '11 -- GMATPrep#2 : 700 (Q47 V38)
23rd Jan '11 -- MGMAT Practice Test #3 : 670 (Q45 V36)
19th Jan '11 -- GMATPrep#1 v.1 : 710 (Q49 V37)
15th Jan '11 -- GMATPrep#1 : 720 (Q47 V42)
11th Jan '11 -- MGMAT Practice Test #2 : 740 (Q47 V44)
6th Jan '11 -- Kaplan#2 : 620 (Q40 V35)
28th Dec '10 -- PowerPrep#1 : 670 (Q47 V35)
30th Oct '10 -- MGMAT Practice Test #1 : 660 (Q45 V35)
12th Sept '10 -- Kaplan Free Test : 610 (Q39 V37)
6th Dec '09 -- PR CAT #1 : 650 (Q44 V37)
25th Oct '09 -- GMATPrep#1 : 620 (Q44 V34)

If you feel like you're under control, you're just not going fast enough.
A goal without a plan is just a wish.
You can go higher, you can go deeper, there are no boundaries above or beneath you.

Intern
Joined: 09 Mar 2010
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

17 Jul 2010, 14:25
Thanks So Much Man. A one point place for reviewing Coordinate Geometry. I have read most of these during EAMCET(Entrance Exam In A.P, India) time , now recollecting all, thanks to you. It would definitely take a long time to Google and learn all these, since most of the books dont cover so deep of a subject. Thanks Again and Keep on doing the great work.
CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 226

Kudos [?]: 1625 [2] , given: 235

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

18 Jul 2010, 04:41
2
KUDOS
For parabola if a = +ve it will open upwards
Open upwards means U....which is smiling
Attachment:

happy.jpg [ 2.43 KiB | Viewed 27954 times ]

If a = -ve...it will open downwards
Open downwards means its unhappy
Attachment:

sad.jpg [ 1.65 KiB | Viewed 27957 times ]

_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Senior Manager
Status: Current Student
Joined: 14 Oct 2009
Posts: 371
Schools: Chicago Booth 2013, Ross, Duke , Kellogg , Stanford, Haas
Followers: 13

Kudos [?]: 114 [0], given: 53

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

02 Aug 2010, 08:17
Does anyone know how often the GMAT asks for anything beyond basic distance/slope? I have a hard time with these, especially rembering all the formulas, I have never seen a parabola question for example. Is it likely I would need to have this formula memorized?
_________________
Intern
Joined: 03 Aug 2010
Posts: 22
Followers: 0

Kudos [?]: 1 [0], given: 0

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

31 Aug 2010, 21:53
I guess this is typo mistake
Correct me if I am wrong

Your post is amazing
_________________

Welcome to my paintings website - Wholesale Art Mall.

CEO
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2795
Location: Malaysia
Concentration: Technology, Entrepreneurship
Schools: ISB '15 (M)
GMAT 1: 670 Q49 V31
GMAT 2: 710 Q50 V35
Followers: 226

Kudos [?]: 1625 [0], given: 235

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

30 Sep 2010, 05:40
Bunnel:

Suppose we have two lines ax+by+c = 0

and 2ax+2by+2c = 0 and question is- are they parallel? I know both are same lines, but do we can them parallel?

In DS question the answer of- are they parallel should be NO? or Yes.
_________________

Fight for your dreams :For all those who fear from Verbal- lets give it a fight

Money Saved is the Money Earned

Jo Bole So Nihaal , Sat Shri Akaal

Support GMAT Club by putting a GMAT Club badge on your blog/Facebook

GMAT Club Premium Membership - big benefits and savings

Gmat test review :
http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html

Math Expert
Joined: 02 Sep 2009
Posts: 36638
Followers: 7106

Kudos [?]: 93656 [0], given: 10583

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

30 Sep 2010, 06:17
gurpreetsingh wrote:
Bunnel:

Suppose we have two lines ax+by+c = 0

and 2ax+2by+2c = 0 and question is- are they parallel? I know both are same lines, but do we can them parallel?

In DS question the answer of- are they parallel should be NO? or Yes.

Basically you are asking whether the line is parallel to itself. It depends how we define the word "parallel". I don't think that there is a consensus about this issue nor that this concept is tested on GMAT. So don't worry about it.
_________________
Intern
Joined: 18 Aug 2010
Posts: 2
Followers: 0

Kudos [?]: 1 [0], given: 3

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

30 Oct 2010, 08:56
Hi all,

Could you please explain how we can solve the below question.
If two lines are intersecting at point (10,27) and equation of one line is y=3x-3
What is the equation of another line.
Intern
Joined: 01 Jun 2009
Posts: 38
Location: Pune, India
Schools: ISB
Followers: 1

Kudos [?]: 4 [1] , given: 2

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

31 Oct 2010, 11:55
1
KUDOS
to solve this que, u must need the slope of the another line... for example if these 2 lines are perpendicular or at an angle, say 30 degree.. then only u'll be able to find the equation of the second line.

so, if it a DS question, your ans sud be E both the statement together r not sufficient

If u like the post, please consider KUDOS.. Thanks

diptich12 wrote:
Hi all,

Could you please explain how we can solve the below question.
If two lines are intersecting at point (10,27) and equation of one line is y=3x-3
What is the equation of another line.
Manager
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 182
Schools: Pitt, Oregon, LBS...
Followers: 33

Kudos [?]: 418 [0], given: 36

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

02 Nov 2010, 12:46
Just what i needed, thanks!
+1!
_________________

[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight]
http://gmatclub.com/forum/massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight]
http://gmatclub.com/forum/1001-ds-questions-file-106193.html#p832133

Intern
Joined: 01 Jun 2009
Posts: 38
Location: Pune, India
Schools: ISB
Followers: 1

Kudos [?]: 4 [0], given: 2

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

03 Nov 2010, 05:05
thanks
Intern
Status: Current Student
Joined: 16 May 2010
Posts: 44
Schools: Darden '13
Followers: 0

Kudos [?]: 9 [1] , given: 4

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

06 Nov 2010, 18:55
1
KUDOS
Seriously awesome. I think your coordinate geometry breakdown is better than MGMAT and Jeff Sackman's Total GMAT Math. This post helped me a ton. Thank you.
Manager
Joined: 01 Nov 2010
Posts: 181
Location: Zürich, Switzerland
Followers: 2

Kudos [?]: 38 [1] , given: 20

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

11 Nov 2010, 14:45
1
KUDOS
Quote:
1. If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.

2. If the slope of line is positive, line WILL intersect quadrants I and III. Y and X intersects of the line with positive slope have opposite signs. Therefore if X intersect is negative, line intersects the quadrant II too, if positive quadrant IV.

3. Every line (but the one crosses origin OR parallel to X or Y axis OR X and Y axis themselves) crosses three quadrants. Only the line which crosses origin OR is parallel to either of axis crosses only two quadrants.

4. If a line is horizontal it has a slope of , is parallel to X-axis and crosses quadrant I and II if the Y intersect is positive OR quadrants III and IV, if the Y intersect is negative. Equation of such line is y=b, where b is y intersect.

5. If a line is vertical, the slope is not defined, line is parallel to Y-axis and crosses quadrant I and IV, if the X intersect is positive and quadrant II and III, if the X intersect is negative. Equation of such line is , where a is x-intercept.

Hi Bunuel, Small corrections here- some of the words need to be intercepts and not intersect.

Cheers!
Sarang
Intern
Joined: 01 Oct 2010
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

12 Nov 2010, 07:58
awesome stuff!!
Can't possibly thank you enough
Director
Joined: 21 Dec 2010
Posts: 649
Followers: 17

Kudos [?]: 219 [0], given: 51

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

31 Jan 2011, 08:56
hmmm. this is good work . very helpful .
_________________

What is of supreme importance in war is to attack the enemy's strategy.

Manager
Joined: 19 Dec 2010
Posts: 145
Followers: 2

Kudos [?]: 29 [0], given: 12

Re: Math: Coordinate Geometry [#permalink]

### Show Tags

01 Apr 2011, 09:04
I had a question regarding this:
Q: Find the equation of a line whose x intercept is 5 and y intercept is 2.
Solution: Substituting the values in equation \frac{x}{a}+\frac{y}{b}=1 we'll get \frac{x}{5}+\frac{y}{2}=1 --> 5y+2x-10=0 OR if we want to write the equation in the slope-intercept form: y=-\frac{2}{5}x+2

Is that right? When you say x intercept is 5 then the points are (0,5) right? Same for y intercept is 2..(2,0).
So when you look at the equation in slope intercept form it should be
y = (-5/2)x + 5
Re: Math: Coordinate Geometry   [#permalink] 01 Apr 2011, 09:04

Go to page   Previous    1   2   3   4    Next  [ 76 posts ]

Similar topics Replies Last post
Similar
Topics:
Coordinate Geometry- 1 24 Mar 2016, 02:15
2 Coordinate geometry 0 02 Sep 2011, 09:30
Coordinate Geometry 2 03 Jun 2011, 08:23
Coordinate Geometry - Syllabus 0 30 Apr 2010, 10:30
1 Coordinate Geometry note 0 22 Apr 2010, 13:34
Display posts from previous: Sort by

# Math: Coordinate Geometry

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.