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Re: If line L passes through point (m, n) and (– m, – n), where m and n [#permalink]

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31 Mar 2011, 05:20

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Pkit wrote:

157. If line L passes through point (m, n) and (– m, – n), where m and n are not 0, which of the following must be true? I. The slope of L is positive II. The slope of L is negative III. L exactly passes through 2 quadrants (A) I only (B) II only (C) III only (D) I and II only (E) II and III only

Equation of the line with slope m passing through point \((x_1,y_1)\) \(&\) \((x_2,y_2)\) \((y-y_1)=m(x-x_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\)

We have the line that is passing through \((m,n)\) \(&\) \((-m,-n)\)

\(Slope=\frac{-n-n}{-m-m}=\frac{n}{m}\)

Equation of the line will be: \(y-n=\frac{n}{m}(x-m)\) \(y-n=\frac{n}{m}x-n\) \(y=\frac{n}{m}x\)

Thus we know that this line passes through the origin as the y-intercept is 0. This makes III true.

If we put, n=1 and m=1 \(y=x\); this line has a positive slope. We can count II out.

Put n=-1 and m=1 \(y=-x\); this line has negative slope. We can count I out.

Re: If line L passes through point (m, n) and (– m, – n), where m and n [#permalink]

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31 Mar 2011, 07:56

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this means that L exactly passes through 2 quadrants. these quadrants are:1,3 or 2,4 <see picture;> and L:y=x (for quadrants 1&3)==>slop=1 (positive) and L:y=-x (for quadrants 2&4)==>slop=-1 (negative) therfore, the correct answer is C;

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Re: If line L passes through point (m, n) and (– m, – n), where m and n [#permalink]

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02 Mar 2016, 10:03

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