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# Math: Coordinate Geometry

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Manager
Joined: 01 Nov 2010
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11 Nov 2010, 15:45
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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

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01 Apr 2011, 15:14
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rachy wrote:
echoing 'MateoLibre' - it is indeed a v helpful post. I have a DS Q....(source: GMATPrep CAT)

In the xy plane at what 2 points does the graph of y = (x+a)(x+b) intersect the x axis?

1] a+b = -1
2] the graph intersects the y axis at (0,-6)

ANY help on how to solve this would be much appreciated. thanks.

This one is a very interesting problem, let us approach it in steps.

you are given y = (x+a)(x+b) and asked when this will intersect the x axis.
Anytime you see "intersect the x axis", you know that y=0
So set y=0 and solve (x+a)(x+b)=0
you get x^2 + x (a+b) + ab = 0

Now look at the statements...
1) gives you a+b, but we don't know what ab is...INSUFF
2) gives you "intersects the y axis @ (0,-6).

So in original statement:
y = (x+a)(x+b) ---> plug in (0,-6)
You will get ab value. but this is INSUFF because we don't know a+b

So, answer is C since you need both 1 and 2 to solve.

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26 Jul 2012, 06:19
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Expert's post
Stiv wrote:
When I have two points in a coordinate system e.g. (2,3) and (6,7) that pass through a line how do I know which number is x1 and which is x2 when calculating slope. Also, the same for the y1 and y2?

It doesn't matter: $$slope=\frac{7-3}{6-2}=\frac{3-7}{2-6}=1$$.
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22 Mar 2017, 23:52
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mesutthefail wrote:

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.
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06 Sep 2017, 21:34
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Expert's post
BloomingLotus wrote:
Hi Bunuel,

Under heading Line equation in Co-ordinate Geometry -

The equation of a straight line passing through points P1(x1,y1)P1(x1,y1) and P2(x2,y2)P2(x2,y2) is:

$$\frac{y−y1}{x−x1}=\frac{y1−y2}{x1−x2}$$

I think it should be :

$$\frac{y−y1}{x−x1}=\frac{y2−y1}{x2−x1}$$

This is because slope for two points is : $$\frac{y2-y1}{x2-x1}$$

Let me know if I am missing anything here.

Both are the same: $$\frac{y2−y1}{x2−x1}=\frac{-(y1−y2)}{-(x1−x2)}=\frac{y1-y2}{x1-x2}$$
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12 Sep 2017, 21:00
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SandhyAvinash wrote:
Can anyone guide me where i can practice only coordinate plane questions??

Use our search engine to find questions from specific category: https://gmatclub.com/forum/search.php?view=search_tags
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06 Dec 2009, 06:27
Here you come again!!!

Kudooossss!!!!!!!!!!!!!!!!!!

You are definitely member of the year. Fingers crossed for the next lesson.
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07 Dec 2009, 18:12
Wow this is amazing

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14 Dec 2009, 07:27
It seems to me that you are in a mission to make us kill the GMAT without cheating as our friends on the other side of the Pacific do.

I promise that I will not let you down

Great Job!

Thanks

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18 Dec 2009, 12:46
No worries Bunuel. The work that you and others are doing is anyways commendable since it is benefitting so many (including me)... Even though questions are taken from various sources, one would not go and check even if the source were known...

cheers,
Kaptain

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26 Jan 2010, 02:21
defoue wrote:
Hi guys,
something I am missing.. why do we do a minus Xc (which is 12) as below for parallel lines???? is it always the case???

Slope AB=\frac{20-7}{5-30}=-052

For the line to be parallel to AB it will have the same slope, and will pass through a given point, C(12,10). We therefore have enough information to define the line by it's equation in point-slope form form:

y=-0.52(x-12)+10 --> y=-0.52x+16.24

The equation of a straight line that passes through a point $$P_1(x_1, y_1)$$ with a
slope $$m$$ is:

$$y-y_1=m(x-x_1)$$

We calculated the slope $$m=-0.52$$, and have the point $$C(12,10)$$. substituting the values in the equation above we get: $$y-10=-0.52(x-12)$$ or $$y=-0.52(x-12)+10$$ as written.

Hope it's clear.
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21 Feb 2010, 08:55
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|.
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27 Jun 2010, 12:09
Great post, cleared the basics of the co-ordinate geometry.

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05 Jul 2010, 07:47
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.)
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17 Jul 2010, 15:25
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.

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02 Aug 2010, 09:17
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?
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31 Aug 2010, 22:53
I guess this is typo mistake
Correct me if I am wrong

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30 Sep 2010, 06:40
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.
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30 Sep 2010, 07:17
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.
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30 Oct 2010, 09:56
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.

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Re: Math: Coordinate Geometry   [#permalink] 30 Oct 2010, 09:56

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