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In the rectangular coordinate system, lines m and n cross at

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In the rectangular coordinate system, lines m and n cross at [#permalink]

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In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?

(1) If the slope of m is y and the slope of n is z, then –yz = 1.

(2) m has a slope of –1, and n passes through the point (–x, –x).
[Reveal] Spoiler: OA

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Re: In the rectangular coordinate system, lines m and n cross at [#permalink]

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New post 23 Sep 2013, 17:03
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b00gigi wrote:
In the rectangular coordinate system, lines m and n cross at the origin. Is line m perpendicular to line n ?

(1) If the slope of m is y and the slope of n is z, then –yz = 1.

(2) m has a slope of –1, and n passes through the point (–x, –x).

Dear b00gigi,
I'm happy to help with this. :-)

You may find these blogs helpful:
http://magoosh.com/gmat/2012/gmat-math- ... x-y-plane/
http://magoosh.com/gmat/2012/gmat-math- ... lar-lines/

In this problem, we know the two lines pass through the origin, (0, 0). That's significant.

Statement #1
If the slope of m is y and the slope of n is z, then –yz = 1.
Perpendicular lines in the x-y plan have slopes that are negative reciprocals. For example,
If one has a slope = 7, the perpendicular line has a slope of –1/7
If one has a slope = 3/5, the perpendicular line has a slope of –5/3
If one has a slope = –4, the perpendicular line has a slope of +1/4
If one has a slope = –8/11, the perpendicular line has a slope of +11/8
Another way to say that is: the product of the slopes of perpendicular lines is -1. Well, if –yz = 1, then yz = –1, and the lines are perpendicular.
This statement, alone and by itself, was enough to answer the prompt question, so it is sufficient.

Statement #2
m has a slope of –1, and n passes through the point (–x, –x).
OK, so the slope of line m is –1. Put that on hold.
If n passes through (–x, –x) and (0, 0), then change in y equals change in x, and the slope is +1. Thus, it is perpendicular to line m.
This statement, alone and by itself, was enough to answer the prompt question, so it is sufficient.

Answer = (D)

Does all this make sense?
Mike :-)
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Mike McGarry
Magoosh Test Prep

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Re: In the rectangular coordinate system, lines m and n cross at [#permalink]

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New post 10 Nov 2013, 03:19
Very helpful explanation......thanks for sharing links
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Re: In the rectangular coordinate system, lines m and n cross at [#permalink]

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New post 19 Oct 2017, 03:18
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Re: In the rectangular coordinate system, lines m and n cross at   [#permalink] 19 Oct 2017, 03:18
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