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 [tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
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
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{3-1}{2-1}[/tex]
[tex]m = \frac{2}{1}[/tex]
[tex]m = 2[/tex]
Line B:
Point 1 (0, 4) x₁ = 0 y₁ = 4
Point 2 (8, 0) x₂ = 8 y₂ = 0
Substitute the information into the formula
[tex]m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]m = \frac{0-4}{8-0}[/tex]
[tex]m = \frac{-4}{8}[/tex]
[tex]m = \frac{-1}{2}[/tex]
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 [tex]\frac{2}{1}[/tex].
Switched top and bottom is [tex]\frac{1}{2}[/tex]
Changed negative sign is [tex]-\frac{1}{2}[/tex]
