The slope of a line can be found with the following expression:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where "m" is the slope and (x1,y1) and (x2,y2) are the points of the line.
When two lines are parallel they have the same slope and when they are perpendicular they have slopes that are the oposite reciprocal of each other. With this in mind let's solve the question.
7. A(0,3), B(5,-7),M(-6,7),N(-2,-1)
Finding the slope of the lines:
[tex]\begin{gathered} m_{AB}=\frac{-7-3}{5-0}=\frac{-10}{5}=-2 \\ m_{MN}=\frac{-1-7}{-2+6}=\frac{-8}{4}=-2 \end{gathered}[/tex]
Since the slopes are equal these lines are parallel.
8. A(-1,4),B(2,-5), M(-3,2),N(3,0)
Finding the slope of the lines:
[tex]\begin{gathered} m_{AB}=\frac{-5-4}{2+1}=\frac{-9}{3}=-3 \\ m_{MN}=\frac{3+3}{0-2}=\frac{6}{-2}=-3 \end{gathered}[/tex]
Since the slopes are equal these lines are parallel.
9. A(-2,-7), B(4,2),M(-2,0),N(2,6)
Finding the slope of the lines:
[tex]\begin{gathered} m_{AB}=\frac{2+7}{4+2}=\frac{9}{6}=\frac{3}{2} \\ m_{MN}=\frac{6-0}{2+2}=\frac{6}{4}=\frac{3}{2} \end{gathered}[/tex]
Since the slopes are equal these lines are parallel.
10. A(-4,-8), B(4,-6), M(-3,5),N(-1,-3)
[tex]\begin{gathered} m_{AB}=\frac{-6+8}{4+4}=\frac{2}{8}=\frac{1}{4} \\ m_{MN}=\frac{-3-5}{-1+3}=\frac{-8}{2}=-4 \end{gathered}[/tex]
Since the slopes areoposite reciprocal of each other these lines are perpendicular
