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].
