Question

which line is perpendicular to a line that has a slope of (\frac{1}{2})?
(\bigcirc) line ab
(\bigcirc) line cd
(\bigcirc) line fg
(\bigcirc) line hj

Explanation:

Step1: Recall perpendicular slope rule

Perpendicular slopes are negative reciprocals. For slope $m=\frac{1}{2}$, perpendicular slope is $m_{\perp} = -\frac{2}{1} = -2$.

Step2: Calculate slope of each line

• Line AB: Use points $A(-4,-3)$ and $B(4,2)$. Slope $m_{AB}=\frac{2-(-3)}{4-(-4)}=\frac{5}{8}$
• Line CD: Use points $C(-4,1)$ and $D(4,-3)$. Slope $m_{CD}=\frac{-3-1}{4-(-4)}=\frac{-4}{8}=-\frac{1}{2}$
• Line FG: Use points $F(-3,-3)$ and $G(0,3)$. Slope $m_{FG}=\frac{3-(-3)}{0-(-3)}=\frac{6}{3}=2$
• Line HJ: Use points $H(-2,3)$ and $J(1,-3)$. Slope $m_{HJ}=\frac{-3-3}{1-(-2)}=\frac{-6}{3}=-2$

Step3: Match to required slope

The slope of line HJ equals $-2$, the negative reciprocal of $\frac{1}{2}$.

Answer:

line HJ