Question

is $overleftrightarrow{ab}$ parallel to $overleftrightarrow{cd}$? explain.
a(0,4)
b(-5,1)
c(5,0)
d(0,-3)
answer attempt 1 out of 2
no, because the slopes are not opposite reciprocal
no, because the slopes are not equal
yes, because both lines have a slope of 3/5
yes, because both lines have a slope of 5/3

Explanation:

Step1: Calculate slope of $\overleftrightarrow{AB}$

The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$. For points $A(0,4)$ and $B(-5,1)$, we have $m_{AB}=\frac{1 - 4}{-5-0}=\frac{-3}{-5}=\frac{3}{5}$.

Step2: Calculate slope of $\overleftrightarrow{CD}$

For points $C(5,0)$ and $D(0,-3)$, using the slope formula $m=\frac{y_2 - y_1}{x_2 - x_1}$, we get $m_{CD}=\frac{-3 - 0}{0 - 5}=\frac{-3}{-5}=\frac{3}{5}$.

Step3: Determine parallel - ness

Two lines are parallel if their slopes are equal. Since $m_{AB}=m_{CD}=\frac{3}{5}$, $\overleftrightarrow{AB}$ is parallel to $\overleftrightarrow{CD}$.

Answer:

yes, because both lines have a slope of 3/5