Answer:
- [tex]\frac{4}{3}[/tex] and [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2-y_{1} } }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 8, 8) and (x₂, y₂ ) = (4, - 8) ← 2 points on green line
m = [tex]\frac{-8-8}{4+8}[/tex] = [tex]\frac{-16}{12}[/tex] = - [tex]\frac{4}{3}[/tex]
Repeat with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (4, 2) ← 2 points on the blue line
m = [tex]\frac{2+1}{4-0}[/tex] = [tex]\frac{3}{4}[/tex]
Since the product of the slopes = - [tex]\frac{4}{3}[/tex] × [tex]\frac{3}{4}[/tex] = - 1
Then the lines are perpendicular
