Question

Use slope to determine if lines AB and CD are parallel, perpendicular, or neither 7. 4(5.-8), B(-2,-10), C(-6, -13). D(-2. 1)m(AB) m(CD) Types of Lines

Answer 1

Let:

A(5,-8)=(x1,y1)

B(-2,-10)=(x2,y2)

m1 = slope of the line AB

$m1=\frac{y2-y1}{x2-x1}=\frac{-10-(-8)}{-2-5}=\frac{-2}{-7}=\frac{2}{7}$

Let:

C(-6, -13)=(x1,y1)

D(-2,1)=(x2,y2)

$m2=\frac{y2-y1}{x2-x1}=\frac{1-(-13)}{-2-6}=\frac{14}{-8}=-\frac{7}{4}$

Now:

$\begin{gathered} \text{Two lines are parallel if:} \\ m1=m2 \\ \text{Two lines are perpendicular if:} \\ m1\cdot m2=-1 \end{gathered}$

So:

$\begin{gathered} \frac{2}{7}\ne-\frac{7}{4} \\ \text{They are not parallel} \\ \frac{2}{7}\cdot(-\frac{7}{4})=-\frac{1}{2}\ne-1 \\ \text{They are not perpendicular} \end{gathered}$