Question

devin incorrectly stated that $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$ for a(-2, 0), b, (2, 3), c(1, -4) and d(5, -1) are neither parallel nor perpendicular.
devins work is shown below.
slope of $overleftrightarrow{ab}$: $\frac{3 - 0}{2 - (-2)} = \frac{3}{4}$
slope of $overleftrightarrow{cd}$: $\frac{-1-(-4)}{1-5} = \frac{3}{-4} = -\frac{3}{4}$
what is the correct relationship between lines $overleftrightarrow{ab}$ and $overleftrightarrow{cd}$? show work to justify your answer.

Explanation:

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

Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$
For $A(-2,0), B(2,3)$:
$m_{AB} = \frac{3 - 0}{2 - (-2)} = \frac{3}{4}$

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

For $C(1,-4), D(5,-1)$:
$m_{CD} = \frac{-1 - (-4)}{5 - 1} = \frac{3}{4}$

Step3: Compare slopes

Parallel lines have equal slopes.
$m_{AB} = m_{CD} = \frac{3}{4}$

Answer:

Lines $\overleftrightarrow{AB}$ and $\overleftrightarrow{CD}$ are parallel, as they have identical slopes of $\frac{3}{4}$.