Question

Use the slopes of lines A and B to show that they are perpendicular to the given line.

Answer 1

Answer:

Line A m = 2

Line B m = -1/2

Lines that are negative reciprocals are perpendicular

Step-by-step explanation:

1. Choose two points from each line.

2. Calculate the slope of each line using formula $m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

3. Check for negative reciprocals

Line A:

Point 1 (1, 1)       x₁ = 1    y₁ = 1

Point 2 (2, 3)     x₂ = 2   y₂ = 3

Substitute the information into the formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \frac{3-1}{2-1}$

$m = \frac{2}{1}$

$m = 2$

Line B:

Point 1 (0, 4)       x₁ = 0    y₁ = 4

Point 2 (8, 0)     x₂ = 8   y₂ = 0

Substitute the information into the formula

$m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m = \frac{0-4}{8-0}$

$m = \frac{-4}{8}$

$m = \frac{-1}{2}$

The slopes are 2 and -1/2. Since they are negative reciprocals to each other, Line A is perpendicular to Line B.

The negative reciprocal of a number is switching its top and bottom fraction, then changing the negative/positive.

2 in fraction form is $\frac{2}{1}$.

Switched top and bottom is $\frac{1}{2}$

Changed negative sign is $-\frac{1}{2}$