Question

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

Answer 1

Slope of AC = -1/4

Slope of BD = 2

AC is not perpendicular to BD.

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 = (y2 - y1)/(x2 - x1)`

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

B = (x1, y1), & C = (x2, y2)

`m_(AC) = (y2 - y1)/(x2 - x1)`

`m_(AC) = (2 - 1)/(-2 - 2) = (1)/(-4)`

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

`m_(BD) = (y2 - y1)/(x2 - x1)`

`m_(BD) = (0 - 4)/(-3 - (-1)) = (-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.