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Segment [tex]\( AB \)[/tex] falls on the line [tex]\( 6x + 3y = 9 \)[/tex]. Segment [tex]\( CD \)[/tex] falls on the line [tex]\( 4x + 2y = 8 \)[/tex].

What is true about segments [tex]\( AB \)[/tex] and [tex]\( CD \)[/tex]?

A. They are parallel because they have the same slope of -2.
B. They are perpendicular because they have slopes that are opposite reciprocals of -2 and [tex]\(\frac{1}{2}\)[/tex].
C. They are parallel because they have the same slope of 2.
D. They are perpendicular because they have opposite reciprocal slopes of 2 and [tex]\(-\frac{1}{2}\)[/tex].

Sagot :

GinnyAnswer
To determine the relationship between segments [tex]\(AB\)[/tex] and [tex]\(CD\)[/tex], we need to find the slopes of the lines on which these segments lie.

First, let's calculate the slope of the line [tex]\(6x + 3y = 9\)[/tex].

1. Rewrite the line in the slope-intercept form [tex]\(y = mx + b\)[/tex], where [tex]\(m\)[/tex] is the slope.
[tex]\[ 6x + 3y = 9 \implies 3y = -6x + 9 \implies y = -2x + 3 \][/tex]
The slope [tex]\(m_1\)[/tex] for this line is [tex]\(-2\)[/tex].

Next, let's calculate the slope of the line [tex]\(4x + 2y = 8\)[/tex].

2. Again, we rewrite this line in the slope-intercept form.
[tex]\[ 4x + 2y = 8 \implies 2y = -4x + 8 \implies y = -2x + 4 \][/tex]
The slope [tex]\(m_2\)[/tex] for this line is also [tex]\(-2\)[/tex].

Since both lines have the same slope, we can conclude that the segments [tex]\(AB\)[/tex] and [tex]\(CD\)[/tex] are parallel.

Therefore, the correct statement is:
- They are parallel because they have the same slope of [tex]\(-2\)[/tex].
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