Answer:
Perpendicular
Step-by-step explanation:
Remember that:
- Two lines are parallel if their slopes are the same.
- Two lines are perpendicular is their slopes are negative reciprocals.
- And two lines are neither (a.k.a intersecting) if they are neither parallel nor perpendicular.
So, let's find the slope of QR and ST.
QR)
We can use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Let Q(-6, 11) be (x₁, y₁) and R(2, -1) be (x₂, y₂). Substitute:
[tex]m=\frac{-1-11}{2-(-6)}[/tex]
Subtract:
[tex]m=-12/8=-3/2[/tex]
So, the slope of QR is -3/2.
ST)
Let S(-4, 8) be (x₁, y₁) and T(-1, 10) be (x₂, y₂). Substitute:
[tex]m=\frac{10-8}{-1-(-4)}[/tex]
Subtract:
[tex]m=2/3[/tex]
So, the slope of ST is 2/3.
The negative reciprocal of -3/2 is 2/3.
And the negative reciprocal of 2/3 is -3/2.
So, the slopes are indeed negative reciprocals of each other.
So, QR and ST are perpendicular.
