Question

Given the lines AB and CD, what conclusion can be made about the relationship of the lines? Be sure to include, in

Answer 1

Answer: They are perpendicular lines, because their slopes are negative reciprocals ($AB\perp CD$)

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

First, find the slope of the line AB. The steps are:

- Choose two points on the line. These can be:

$(0,-1)\\(5,3)$

You can say that:

$y_2=-1\\y_1=3\\\\x_2=0\\x_1=5$

Substituting values into the formula and evaluating, you get that the slope of this line is:

$m_{AB}=\frac{-1-3}{0-5}=\frac{4}{5}$

Now you must find the slope of the line CD. The steps are shown below:

- Choose two points on the line. These can be:

$(2,3)\\(6,-2)$

- You can say that:

$y_2=-2\\y_1=3\\\\x_2=6\\x_1=2$

- Now you must substitute values into the formula and evaluate, in order to find the slope. This is:

$m_{CD}=\frac{-2-3}{6-2}=-\frac{5}{4}$

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.