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# In the xy-plane, line l and line k intersect at the point

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Manager
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In the xy-plane, line l and line k intersect at the point [#permalink]

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26 Sep 2010, 11:49
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In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?

(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.
[Reveal] Spoiler: OA

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26 Sep 2010, 12:19
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udaymathapati wrote:
In the xy-plane, line l and line k intersect at the point (16/5, 12/5). What is the slope of line l?
(1) The product of the slopes of line l and line k is –1.
(2) Line k passes through the origin.

Line $$l$$ passes through the point (16/5, 12/5). If we knew some other point through which line $$l$$ passes then we would be able to calculate the slope: 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.

(1) The product of the slopes of line $$l$$ and line $$k$$ is -1 --> line $$l$$ and $$k$$ are perpendicular to each other (the two lines are perpendicular if and only the product of their slopes is -1). Not, sufficient, as we can have infinite # of perpendicular lines passing through some point (16/5, 12/5).

(2) Line $$k$$ passes through the origin --> we have the second point for line $$k$$, so we can calculate the slope of $$k$$, but we don't know the relationship between the lines $$l$$ and $$k$$. Not sufficient.

(1)+(2) We can calculate the slope of $$k$$ and we know that the product of the slopes of $$l$$ and $$k$$ is -1, so we can calculate the slope of line $$l$$ too. Sufficient.

For more on these issues check Coordinate Geometry chapter of Math Book (link in my signature).

Hope it helps.
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Manager
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26 Sep 2010, 12:22
We know one point in the coordinate system.

(1) Insufficient. First, you must know that perpendicular lines have negative reciprocal slopes. We know that the product of the slopes of l and k is -1, therefore they are perpendicular.

(2) Insufficient. We can now solve for the slope of k, but we know nothing about l.

(1+2) Sufficient, Since we know the slope of k, then we know the slope of l is -1/k.

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Manager
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26 Sep 2010, 12:24
Bunuel, you are too quick!

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14 Oct 2010, 19:34
C

1) says l and k have opposite slopes. so given point is perpendicular point on intersection ==> NOT SUFF though to find the slope

2) point of intersection and origin will give us the slope of k ==> NOT SUFF by itself since we would not know about the perpendicular bisection

1 + 2 ==> -1/slope of k == slope of l ==> SUFF
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Re: In the xy-plane, line l and line k intersect at the point [#permalink]

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16 Oct 2013, 00:38
Hello from the GMAT Club BumpBot!

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Re: In the xy-plane, line l and line k intersect at the point [#permalink]

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01 Sep 2015, 00:41
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).

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Re: In the xy-plane, line l and line k intersect at the point   [#permalink] 01 Sep 2015, 00:41
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