Answer: They are perpendicular lines, because their slopes are negative reciprocals ([tex]AB\perp CD[/tex])
Step-by-step explanation:
The missing graph is attached.
You need to remember that the slope of a line can be found with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
First, find the slope of the line AB. The steps are:
- Choose two points on the line. These can be:
[tex](0,-1)\\(5,3)[/tex]
You can say that:
[tex]y_2=-1\\y_1=3\\\\x_2=0\\x_1=5[/tex]
Substituting values into the formula and evaluating, you get that the slope of this line is:
[tex]m_{AB}=\frac{-1-3}{0-5}=\frac{4}{5}[/tex]
Now you must find the slope of the line CD. The steps are shown below:
- Choose two points on the line. These can be:
[tex](2,3)\\(6,-2)[/tex]
- You can say that:
[tex]y_2=-2\\y_1=3\\\\x_2=6\\x_1=2[/tex]
- Now you must substitute values into the formula and evaluate, in order to find the slope. This is:
[tex]m_{CD}=\frac{-2-3}{6-2}=-\frac{5}{4}[/tex]
By definition, the slopes of perpendicular lines are negative reciprocals.
Therefore, since the slopes of the lines AB and CD are negative reciprocals, you can conclude that they are perpendicular.
