ScholarDen Representative
Joined: 21 Aug 2021
Posts: 119
Given Kudos: 6
Two points, G and J with coordinates (c, d) and (m, n)
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08 Dec 2021, 23:35
Solution:
Let's explore each option on an individual basis here:
Option A)
c < m < 0
Let's take the point G as (c, d) implies (-5, 0) and the point J as (m, n) implies (-4, 2), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = 2−0−4−(−5) = 2
Therefore, this option may be true.
Option B)
d > n > 0
Let's take the point G as (c, d) implies (-5, 3) and the point J as (m, n) implies (-4, 1), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = 3−1−5−(−4) = -2
Similarly, if we take the point G as (c, d) implies (5, 10) and the point J as (m, n) implies (7, 8), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = 10−85−7= -1
That's why, this option can not be true.
Option C)
n > d > 0
The points G and J can fall in the 1st or 2nd quadrant. Let's take the point G as (c, d) implies (-6, 7) and the point J as (m, n) implies (-4, 9), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = 9−7−4−(−6) = 2
Therefore, this option can be true.
Option D)
n = 0
We can assume the point G as (c, d) implies (-6, 6) and the point J as (m, n) implies (-4, 0), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = 6−0−6−(−4) = -3
Similarly, if we take the point G as (c, d) implies (-6, -6) and the point J as (m, n) implies (-4, 0), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = −6−0−6−(−4)= 3
Therefore, this option can be true.
Option E)
d < 0 < n
Let's take the point G as (c, d) implies (-5, -2) and the point J as (m, n) implies (-3, 2), then the slope will be:
Slope of line ¯GJ = ΔyΔx
Slope of line ¯GJ = 2−(−2)−3−(−5) = 2
That's why, this option may be true as well.
Hence, the correct answers are Option A), C), D) and E).
28% (02:12) correct
