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If line L passes through point (m, n) and (– m, – n), where m and n ar 16 Jun 2019, 23:52
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C
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65% (hard)

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49% (01:34) correct 51% (01:37) wrong based on 135 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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C
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If line L passes through point (m, n) and (– m, – n), where m and n ar Updated on: 30 Sep 2020, 01:06
Originally posted by firas92 on 17 Jun 2019, 00:16.
Last edited by firas92 on 30 Sep 2020, 01:06, edited 4 times in total.
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Bunuel
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
Show more

The slope of the line L = n/m where each of n and m can be positive or negative

This means n/m can be positive or negative and so we can eliminate statements I and II

We are left with Statement III only

Answer is (C)
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If line L passes through point (m, n) and (– m, – n), where m and n ar 17 Jun 2019, 03:03
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The slope be y2-y1/x2-x1. This gives us (n-(-n)/m-(-m)= 2n/2m which gives us n/m. Now if n is positive and m is positive, the slope is positive.If either n or m is negative the slope is negative. So the slope could be negative or positive depending on the values of m or n.Eliminate all answers containing I or II. The answer is thus III,C.
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If line L passes through point (m, n) and (– m, – n), where m and n ar 17 Jun 2019, 08:37
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Bunuel
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
Show more

plot a graph and visualize
IMO C is only correct ; other two options are not possible as value of slope would vary with value of n & m
IMO C
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If line L passes through point (m, n) and (– m, – n), where m and n ar 23 Sep 2020, 21:49
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Concept: When you take a Point (X, Y) and Reflect the Point over the Origin (0 , 0) ---- You Negate the Sign of Each Coordinate, such that it becomes (-X , -Y)

No matter which Quadrant you start from, because you are Reflecting over the Origin, the Point will end up as the "MIRROR" Point in the Vertically Opposite Quadrant

The Slope can either be (+)Positive or (-)Negative, but no matter which 2 Points you choose, because the Points are "Mirror Images" Reflected over the Origin, the Line will always pass through the Origin (0 , 0).

Any Line that passes through the Origin (other than Horizontal or Vertical Lines) will ONLY Pass through 2 Quadrants.


Only III MUST be True.

-C-
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If line L passes through point (m, n) and (– m, – n), where m and n ar 02 Feb 2025, 00:32
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