Question

are bc and ad parallel? a(-4,1) b(-1,3) c(3,1) d(1,-1) a. yes b. no

Explanation:

Step1: Find slope of BC

The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $B(-1,3)$ and $C(3,1)$, we have $m_{BC}=\frac{1 - 3}{3-(-1)}=\frac{-2}{4}=-\frac{1}{2}$.

Step2: Find slope of AD

For points $A(-4,1)$ and $D(0,-1)$, we use the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m_{AD}=\frac{-1 - 1}{0-(-4)}=\frac{-2}{4}=-\frac{1}{2}$.

Step3: Check parallel - slope condition

Two lines are parallel if and only if their slopes are equal. Since $m_{BC}=m_{AD}=-\frac{1}{2}$, lines BC and AD are parallel.

Answer:

A. yes