Answer:
lines are perpendicular
Step-by-step explanation:
Parallel lines have equal slopes
The product of the slopes of perpendicular lines = - 1
Calculate the slopes m of the 2 lines using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (7, 3 ) and (x₂, y₂ ) = (8, 7 )
m = [tex]\frac{7-3}{8-7}[/tex] = [tex]\frac{4}{1}[/tex] = 4
Repeat with
(x₁, y₁ ) = (- 5, - 4 ) and (x₂, y₂ ) = (- 1, - 5 )
m = [tex]\frac{-5-(-4)}{-1-(-5)}[/tex] = [tex]\frac{-5+4}{-1+5}[/tex] = [tex]\frac{-1}{4}[/tex] = - [tex]\frac{1}{4}[/tex]
Slopes are not equal so lines are not parallel
4 × - [tex]\frac{1}{4}[/tex] = - 1
Then the 2 lines are perpendicular to each other
