Question

Determine whether the lines are passing through the pairs of points are parallel, perpendicular, or neither.

Answer 1

Given:

$\begin{gathered} L_1:(1,-3),(4,12) \\ L_2:(3,4),(13,2) \end{gathered}$

Required:

Find whether the lines passing through the pairs of points are parallel, perpendicular, or neither.

Explanation:

The slope of the line

$L_1$$\begin{gathered} m_1=\frac{12-(-3)}{4-1} \\ =\frac{15}{3} \\ =5 \end{gathered}$

The slope of the line

$L_2$$\begin{gathered} m_2=\frac{2-4}{13-3} \\ =\frac{-2}{10} \\ =-\frac{1}{5} \end{gathered}$

The product of the slopes is:

$\begin{gathered} m_1m_2=5\times-\frac{1}{5} \\ =-1 \end{gathered}$

The product of the slope is -1 so the lines will be perpendicular.

Final Answer:

The second option is the correct answer.