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Re: Math: Coordinate Geometry
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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...... intherectangularcoordinatesystemshownabovedoesthe90635.htmlArchit 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. Attachment:
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Re: Math: Coordinate Geometry
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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....
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10 Feb 2013, 04:23



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Re: Math: Coordinate Geometry
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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 y2y1 / x2x1
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?



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Re: Math: Coordinate Geometry
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22 Mar 2017, 22:52
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 y2y1 / x2x1
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 ab = (ba). Did you get this rule?? Now, in a similar way if you take  sign common from both numerator and denominator of y2y1 / x2x1, you will get (y1y2)/(x1x2). 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 = (y1y2)/(x1x2). I hope that makes sense.
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Re: Math: Coordinate Geometry
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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 y2y1 / x2x1
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) \(Slope = \frac{(y2  y1)}{(x2  x1)} = \frac{10  3}{5  2} = \frac{13}{3}\) \(Slope = \frac{(y1  y2)}{(x1  x2)} = \frac{3 (10)}{2  5} = \frac{13}{3}\)
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Re: Math: Coordinate Geometry
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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?



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Re: Math: Coordinate Geometry
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06 Sep 2017, 17:11
Hi Bunuel, Under heading Line equation in Coordinate 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 : \(\frac{y2y1}{x2x1}\) Let me know if I am missing anything here.



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06 Sep 2017, 20:34



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Re: Math: Coordinate Geometry
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22 Aug 2018, 19:40
Bunuel wrote: 4. Intercept form. The equation of a straight line whose x and y intercepts are a and b, respectively, is: \(\frac{x}{a}+\frac{y}{b}=1\)
Example #3 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 \(\frac{x}{5}+\frac{y}{2}=1\) > \(5y+2x10=0\) OR if we want to write the equation in the slopeintercept form: \(y=\frac{2}{5}x+2\)
I can't figure out how you got the 10 in this 5y+2x10=0 from \(\frac{x}{5}+\frac{y}{2}=1\)



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22 Aug 2018, 20:31



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15 Sep 2018, 23:54
Dear Bunuel, Thanks for the wonderful explanation of coordinate geometry. The math guide is a surely a saviour. I just wanted to bring your attention to the below quote, which is mentioned in the book. Quote: A horizontal line has a slope of zero. The equation of a horizontal line is: y=b Where: x is the coordinate of any point on the line; b is where the line crosses the yaxis (y intercept). Notice that the equation is independent of x. Any point on the horizontal line satisfies the equation. I think the highlighted text in red should be y instead of x. Thanks



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