Question

The lines shown below are perpendicular.
5
(-2,4)
4
(2.1)
5
(0,-2)
(-4,-2)
A. True
B. False

Answer 1

Answer:

False. The two lines in this diagram are not perpendicular with one another.

Step-by-step explanation:

Two lines in a plane are perpendicular if and only the product of their slopes is $(-1)$.

If a non-vertical line in a plane goes through two points, $(x_{0},\, y_{0})$ and $(x_{1},\, y_{1})$ ($x_{0} \ne y_{0}$,) the slope of this line would be:

$\begin{aligned}m &= \frac{y_{0} - y_{1}}{x_{0} - x_{1}}\end{aligned}$.

Find the slope of the two lines given the coordinates of the points.

Slope of the line sloping downwards:

$\begin{aligned}m_{a} &= \frac{4 - (-2)}{(-2) - 0} \\ &= \frac{6}{(-2)} \\ &= (-3)\end{aligned}$.

Slope of the line sloping upwards:

$\begin{aligned}m_{b} &= \frac{1 - (-2)}{2 - (-4)} \\ &= \frac{3}{6} \\ &= \frac{1}{2}\end{aligned}$.

The product of the slopes of the two lines is:

$\begin{aligned}m_{a}\, m_{b} &= (-3) \times \frac{1}{2} \\ &= \left(-\frac{3}{2}\right)\end{aligned}$.

Therefore, these two lines are not perpendicular to one another since the product of their slopes isn't $(-1)$.