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# In the xy-coordinate system, do any points on line k lie in

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In the xy-coordinate system, do any points on line k lie in  [#permalink]

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15 Feb 2012, 16:10
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25% (medium)

Question Stats:

67% (00:55) correct 33% (01:15) wrong based on 543 sessions

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In the xy-coordinate system, do any points on line k lie in quadrant III?

(1) Line k has y-intercept 2

(2) Line k has slope 2/3

Now what will be the step by step approach to attempt this question?

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In the xy-coordinate system, do any points on line k lie in  [#permalink]

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15 Feb 2012, 16:34
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In the xy-coordinate system, do any points on line k lie in quadrant III?

You should just visualize this to solve.

(1) Line k has y-intercept 2 --> if the slope is negative or zero then K will not pass through the III quadrant but if it's positive then it will. Not sufficient.

(2) Line k has slope 2/3 --> any line with positive slope passes through the quadrants I and III. Sufficient.

Check the image below:

Red and blue lines do not pass through III quadrant and green one does. Notice that any line parallel to green line (so with a slope of 2/3) will also pass through III quadrant.

Some notes:
1. If the slope of line is negative, 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, line intersects the quadrant I too, 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 of either of axis crosses two quadrants.

4. If a line is horizontal the line has slope 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.

Check this: http://gmatclub.com/forum/in-the-xy-coo ... 86074.html and this: http://gmatclub.com/forum/math-coordina ... 87652.html for more.

Hope it helps.

Attachment:

graph (2).png [ 8.49 KiB | Viewed 8779 times ]

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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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15 Jan 2013, 03:48
Great bit of theory, Thanks bunuel!
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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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27 Jun 2013, 21:28
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Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

Theory on Coordinate Geometry: math-coordinate-geometry-87652.html

All DS Coordinate Geometry Problems to practice: search.php?search_id=tag&tag_id=41
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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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27 Jun 2013, 22:26
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Dear Bunuel,
I just want to clear my doubt. If the 2nd statement had been " Line K has negative slope" then we would have required both statements together to answer the question. correct??
Regards,
Narenn
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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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27 Jun 2013, 22:31
Narenn wrote:
Dear Bunuel,
I just want to clear my doubt. If the 2nd statement had been " Line K has negative slope" then we would have required both statements together to answer the question. correct??
Regards,
Narenn

Absolutely. Notice that in this case the answer to the question would be NO.
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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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27 Jun 2013, 22:53
hmm.. You are correct.
Thanks
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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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27 Jun 2013, 22:56
Narenn wrote:
hmm.. You are correct.
Thanks

Let me make clear: you are correct the answer would be C, but the answer to the question whether "any points on line k lie in quadrant III" would be NO.
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Re: In the xy-coordinate system, do any points on line k lie in  [#permalink]

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30 Jul 2018, 05:02
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.
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Re: In the xy-coordinate system, do any points on line k lie in &nbs [#permalink] 30 Jul 2018, 05:02
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