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Coordinate Geometry Problem

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by Cedagmat » Sat Nov 13, 2010 5:05 pm
179. If line l passes through point (m,- n), is the slope of the line negative?
(1) The line passes through point (-m, n).
(2) m^n is negative.

Answer: E

S1: If we solve for the slope which is rise/run--> slope = (-n-n)/(m- -m)= -(n/m) which is by definition a negative slope. Sufficient.
S2: This means that m is negative and that n is odd. Insufficient.

Can anyone tell me why S1 is insufficient?
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by Ian Stewart » Sat Nov 13, 2010 7:02 pm
Cedagmat wrote:179. If line l passes through point (m,- n), is the slope of the line negative?
(1) The line passes through point (-m, n).
(2) m^n is negative.

Answer: E

S1: If we solve for the slope which is rise/run--> slope = (-n-n)/(m- -m)= -(n/m) which is by definition a negative slope. Sufficient.
-(n/m) is not necessarily a negative number -- it will be if n and m are both positive, but we're not told that here. If, say, n = -1 and m = 1, then -(n/m) = -(-1/1) = 1.
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by Cedagmat » Sun Nov 14, 2010 11:26 am
So in this case, it does not matter that that problem has stated that the signs associated with m and n?
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by Ian Stewart » Sun Nov 14, 2010 1:12 pm
Cedagmat wrote:So in this case, it does not matter that that problem has stated that the signs associated with m and n?
I'm afraid I don't understand the question; the problem doesn't tell you anything about the signs of m or n.

I think you might be assuming that -m is a negative number here. That's not necessarily true. The expression -m is negative if m is positive, but it's positive when m is negative.
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by Cedagmat » Mon Nov 15, 2010 9:48 am
That answered my question. I though that -m meant that m was a negative number, but I see your point about it being an expression. That definitely explains my error.
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