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If line L passes through point (m, n) and (– m, – n), where m and n
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31 Mar 2011, 05:45
Question Stats:
48% (00:49) correct 52% (01:27) wrong based on 34 sessions
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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
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Re: If line L passes through point (m, n) and (– m, – n), where m and n
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31 Mar 2011, 06:20
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 \((x_1,y_1)\) \(&\) \((x_2,y_2)\) \((yy_1)=m(xx_1)=\frac{y_2y_1}{x_2x_1}(xx_1)\) We have the line that is passing through \((m,n)\) \(&\) \((m,n)\) \(Slope=\frac{nn}{mm}=\frac{n}{m}\) Equation of the line will be: \(yn=\frac{n}{m}(xm)\) \(yn=\frac{n}{m}xn\) \(y=\frac{n}{m}x\) Thus we know that this line passes through the origin as the yintercept 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. Ans: "C"
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Re: If line L passes through point (m, n) and (– m, – n), where m and n
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31 Mar 2011, 06:28
Let (m,n) = (2,3) (m,n) = (2,3) Slope = (3+3)/(2+2) = 6/4 = 3/2 So II may not be true Let (m,n) = (2,3) then (m,n) = (2,3) So slope = (3 +3)/(22) = 3/2 so I may not be true So such a line would be > (y  3) = 3/2(x  2) => 2y  6 = 3x  6 => 2y  3x = 0, hence no x or y intercept, so it passes through origin. III is true. Answer  C
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Re: If line L passes through point (m, n) and (– m, – n), where m and n
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31 Mar 2011, 06:35
@fluke and @PKit, should this be moved to PS forum, doesn't look like a DS question.
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Re: If line L passes through point (m, n) and (– m, – n), where m and n
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31 Mar 2011, 08:56
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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If line L passes through point (m, n) and (– m, – n), where m and n
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03 Sep 2017, 00:38
Since we know nothing about the signs of n and m, we can say nothing for sure about positions of two points on the coordinate plane. Hence options I and II can't be proved.
Lets analyze the III option:
For the line to pass only two quadrants it must either pass trough the origin or be parallel to X or Yaxis. Since the coordinates of two points have different signs, we can eliminate the possibility of parallelism.
Now, try to prove that line passes trough the origin. The equation of a line is y=s*x+b. In order to the line to pass thru the origin, yintercept (e.g. b in the equation) must be zero.
The question becomes whether ys*x=o?
Lets prove it. Find the slope > s=(n(n))/(m(m)) > s=n/m
Put two given points into the equation First point (m, n) > nn/m*m =0 True Second point (m,n) > n  ( n/m*(m))=0 True
Hence answer is C
Agree?




If line L passes through point (m, n) and (– m, – n), where m and n
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03 Sep 2017, 00:38






