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}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
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}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![m = \frac{3-1}{2-1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B3-1%7D%7B2-1%7D)
![m = \frac{2}{1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B2%7D%7B1%7D)
![m = 2](https://tex.z-dn.net/?f=m%20%3D%202)
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}}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_%7B2%7D-y_%7B1%7D%7D%7Bx_%7B2%7D-x_%7B1%7D%7D)
![m = \frac{0-4}{8-0}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B0-4%7D%7B8-0%7D)
![m = \frac{-4}{8}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-4%7D%7B8%7D)
![m = \frac{-1}{2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-1%7D%7B2%7D)
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
.
Switched top and bottom is ![\frac{1}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D)
Changed negative sign is ![-\frac{1}{2}](https://tex.z-dn.net/?f=-%5Cfrac%7B1%7D%7B2%7D)