Question

7. determine which of the lines are parallel and which of the lines are perpendicular

Answer 1

Parallel lines are lines on a plane that never meets. The lines are the same distance apart.

Perpendicular lines form a right angle.

Parallel lines have the same slopes. let's check the slopes of the lines.

$\begin{gathered} \text{ Line p} \\ m_1=\frac{4+1}{1+4}=\frac{5}{5}=1 \\ \text{ Line q} \\ m_2=\frac{-1+4}{3-0}=\frac{3}{3}=1 \\ \text{ Line r} \\ m_3=\frac{1-4}{2+2}=-\frac{3}{4} \\ \text{ line s} \\ m_4=\frac{-2-1}{1+2}=-\frac{3}{3}=-1 \\ \text{ line t} \\ m_5=\frac{-4+1}{0+4}=-\frac{3}{4} \end{gathered}$

As we can see, the lines that are parallel base on the slopes are as follows

$\begin{gathered} p\parallel q \\ r\parallel t \end{gathered}$

Perpendicular lines, the product of their slopes is equals to negative -1.

$\begin{gathered} m_2m_4=-1 \\ 1\times-1=-1 \\ \\ m_1m_4=-1 \\ 1\times-1=-1 \\ \\ \end{gathered}$

Therefore,

$\begin{gathered} p\perp s \\ q\perp s \\ \end{gathered}$