Answer:
The lines blue and green are perpendicular
Step-by-step explanation:
we know that
If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
step 1
Find the slope of the blue line
we have the points
(-1,-3) and (0,3)
substitute
[tex]m=\frac{3+3}{0+1}[/tex]
[tex]m=\frac{6}{1}=6[/tex]
step 2
Find the slope of the red line
we have the points
(3,-3) and (4,2)
substitute
[tex]m=\frac{2+3}{4-3}[/tex]
[tex]m=\frac{5}{1}=5[/tex]
step 3
Find the slope of the green line
we have the points
(-4,-1) and (2,-2)
substitute
[tex]m=\frac{-2+1}{2+4}[/tex]
[tex]m=-\frac{1}{6}[/tex]
step 4
Compare the slopes
Blue line ----> [tex]m=6[/tex]
Red line ----. [tex]m=5[/tex]
Green line ---> [tex]m=-\frac{1}{6}[/tex]
so
The slope of the blue line and the green line are opposite reciprocal ( their product is equal to -1)
therefore
The lines blue and green are perpendicular
