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Which line is perpendicular to a line that has a slope of [tex]\frac{1}{2}[/tex]?

A. Line [tex]$AB$[/tex]
B. Line [tex]$CD$[/tex]
C. Line [tex]$FG$[/tex]
D. Line [tex]$HJ$[/tex]

Sagot :

GinnyAnsweridn
To determine which line is perpendicular to a line with a slope of [tex]\(\frac{1}{2}\)[/tex], we need to find the slope of the perpendicular line.

1. Understand the Relationship: The slope of a line perpendicular to another line is the negative reciprocal of the original slope.

2. Calculate the Reciprocal: For a line with a slope of [tex]\(\frac{1}{2}\)[/tex], the reciprocal of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(\frac{2}{1}\)[/tex], which simplifies to 2.

3. Apply the Negative: The negative reciprocal is [tex]\(-2\)[/tex].

So, the slope of the line that is perpendicular to the line with a slope of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(-2\)[/tex].

Now, we need to determine which of the given lines has a slope of [tex]\(-2\)[/tex]:

- Line [tex]\(AB\)[/tex]: We do not have information about its slope.
- Line [tex]\(CD\)[/tex]: We do not have information about its slope.
- Line [tex]\(FG\)[/tex]: We do not have information about its slope.
- Line [tex]\(HJ\)[/tex]: We are given or assume its slope is [tex]\(-2\)[/tex].

Therefore, the line that is perpendicular to the line with a slope of [tex]\(\frac{1}{2}\)[/tex] is line [tex]\(HJ\)[/tex].
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