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Which line is perpendicular to a line that has a slope of [tex] \frac{1}{2} \text{?} [/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 that has a slope of [tex]\(\frac{1}{2}\)[/tex], we need to find the slope of a line that is perpendicular to it.

1. Given Slope:
The slope of the original line is [tex]\(\frac{1}{2}\)[/tex].

2. Perpendicular Slope:
To find the slope of a line that is perpendicular, we use the concept that the slopes of two perpendicular lines are negative reciprocals of each other.

- The reciprocal of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(2\)[/tex].
- The negative reciprocal of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(-2\)[/tex].

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

So, the line which is perpendicular to a line that has a slope of [tex]\(\frac{1}{2}\)[/tex] would have a slope of [tex]\(-2\)[/tex]. We would need additional information about the slopes of the given lines (AB, CD, FG, HJ) to determine specifically which of those is perpendicular, but the key determinant here is the slope of [tex]\(-2\)[/tex].
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