Question

Find the slope of AC and BD. Decide whether AC is perpendicular to BD.

Answer 1

Answer:

Slope of AC = -1/4

Slope of BD = 2

AC is not perpendicular to BD.

Step-by-step explanation:

Given the following points:

A (2, 1) & C (-2, 2)

B (-1, 4) & D (-3, 0)

Plug these values into the slope formula:

$m = \frac{y2 - y1}{x2 - x1}$

Let A = (x1, y1), & C = (x2, y2)

     B =  (x1, y1), & C = (x2, y2)

$m_{AC} = \frac{y2 - y1}{x2 - x1}$

$m_{AC} = \frac{2 - 1}{-2 - 2} = \frac{1}{-4}$

Therefore, the slope of AC = -1/4.

$m_{BD} = \frac{y2 - y1}{x2 - x1}$

$m_{BD} = \frac{0 - 4}{-3 - (-1)} = \frac{-4}{-2} = 2$

Therefore, the slope of BD = 2.

By definition, perpendicular lines have slopes that are negative reciprocals. This means that when you multiply the slopes of those two lines, it will result in - 1.

By multiplying the slopes of AC and BD, you'll get:

$m_{AC} = -1/4$ × $m_{BD} = 2$  = -1/2

Since the product of the slopes of AC and BD is -1/2, then it means that their lines are not perpendicular because the product of their slopes is not equal to -1.