Answer:
B.) AB and CD are perpendicular lines
Step-by-step explanation:
we have
[tex]A(-8,1),B(-2,4),C(-3,-1),D(-6,5)[/tex]
Verify each statement
A.) A, B, C, and D lie on the same line
The statement is False
To better understand the question plot the points
using a graphing tool
see the attached figure
therefore
The points A, B, C, and D not lie on the same line
B.) AB and CD are perpendicular lines
The statement is True
Because
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal of each other (the product is equal to -1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
Find the slope AB
[tex]A(-8,1), B(-2,4)[/tex]
Substitute the values
[tex]m=\frac{4-1}{-2+8}[/tex]
[tex]m=\frac{3}{6}[/tex]
[tex]m=\frac{1}{2}[/tex]
Find the slope CD
[tex]C(-3,-1),D(-6,5)[/tex]
Substitute the values
[tex]m=\frac{5+1}{-6+3}[/tex]
[tex]m=\frac{6}{-3}[/tex]
[tex]m=-2[/tex]
Find the product of the slopes
[tex]\frac{1}{2}*(-2)=-1[/tex]
therefore
The lines AB and CD are perpendicular
C.) AB and CD are parallel lines.
The statement is False
Because
Lines AB and CD are perpendicular lines (see the part B)
D.) AB and CD are intersecting lines but are not perpendicular
The statement is false
Because
Line AB and line CD are intersecting perpendicular lines (see the part B)
E.) AC and BD are parallel lines
The statement is false
Because
we know that
If two lines are parallel, then their slopes are the same
Find the slope AC
[tex]A(-8,1),C(-3,-1)[/tex]
Substitute the values
[tex]m=\frac{-1-1}{-3+8}[/tex]
[tex]m=\frac{-2}{5}[/tex]
[tex]m=-\frac{2}{5}[/tex]
Find the slope BD
[tex]B(-2,4),D(-6,5)[/tex]
Substitute the values
[tex]m=\frac{5-4}{-6+2}[/tex]
[tex]m=\frac{1}{-4}[/tex]
[tex]m=-\frac{1}{4}[/tex]
Compare the slopes
[tex]-\frac{2}{5}\neq-\frac{1}{4}[/tex]
therefore
AC and BD are not parallel lines
