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 the perpendicular line.
If a line has a slope of [tex]\(\frac{1}{2}\)[/tex], a line perpendicular to it will have a slope that is the negative reciprocal of [tex]\(\frac{1}{2}\)[/tex].
The reciprocal of [tex]\(\frac{1}{2}\)[/tex] is [tex]\(2\)[/tex]. Therefore, the negative reciprocal would be [tex]\( -2 \)[/tex].
Thus, any line that has a slope of [tex]\(-2\)[/tex] is perpendicular to a line with a slope of [tex]\(\frac{1}{2}\)[/tex]. Therefore:
The line [tex]\(A B\)[/tex] is perpendicular to the original line with a slope of [tex]\(\frac{1}{2}\)[/tex].
