Question

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

Answer 1

Answer:

(a)Perpendicular

(b)Parallel

(c)neither parallel nor perpendicular.

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

$\begin{gathered} \text{Slope of }\bar{\text{PQ}}=5 \\ \text{Slope of JK}=-\frac{1}{5} \\ 5\times-\frac{1}{5}=-1 \end{gathered}$

Lines PQ and JK are perpendicular.

Part B

$\begin{gathered} \text{Slope of EF}=-\frac{3}{4} \\ \text{Slope of CD}=-\frac{3}{4} \\ -\frac{3}{4}=-\frac{3}{4} \end{gathered}$

Lines EF and CD are parallel.

Part B

$\begin{gathered} \text{Slope of WX}=\frac{1}{2} \\ \text{Slope of YZ}=-\frac{1}{2} \end{gathered}$

Lines WX and YZ are neither parallel nor perpendicular.

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