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=(y2-y1)/(x2-x1)=(-10-(-8))/(-2-5)=(-2)/(-7)=(2)/(7)`

Let:

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

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

`m2=(y2-y1)/(x2-x1)=(1-(-13))/(-2-6)=(14)/(-8)=-(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} (2)/(7)\\e-(7)/(4) \\ \text{They are not parallel} \\ (2)/(7)\cdot(-(7)/(4))=-(1)/(2)\\e-1 \\ \text{They are not perpendicular} \end{gathered}`