Question

Determine whether the lines are parallel, perpendicular, intersect, or coincide.

Answer 1

(a)Perpendicular

(b)Parallel

(c)neither parallel nor perpendicular.

Step-by-step explanation:

Definition

• Two lines are ,parallel, if they have the ,same slope.

,

• Two lines are ,perpendicular, if the ,product of their slopes is -1.

Part A

`\begin{gathered} \text{Slope of }\bar{\text{PQ}}=5 \\ \text{Slope of JK}=-(1)/(5) \\ 5*-(1)/(5)=-1 \end{gathered}`

Lines PQ and JK are perpendicular.

Part B

`\begin{gathered} \text{Slope of EF}=-(3)/(4) \\ \text{Slope of CD}=-(3)/(4) \\ -(3)/(4)=-(3)/(4) \end{gathered}`

Lines EF and CD are parallel.

Part B

`\begin{gathered} \text{Slope of WX}=(1)/(2) \\ \text{Slope of YZ}=-(1)/(2) \end{gathered}`

Lines WX and YZ are neither parallel nor perpendicular.

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