Question

Question 17

Answer 1

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:

$m=\frac{y_2-y_1}{x_2-x_1}$

Let Q(-6, 11) be (x₁, y₁) and R(2, -1) be (x₂, y₂). Substitute:

$m=\frac{-1-11}{2-(-6)}$

Subtract:

$m=-12/8=-3/2$

So, the slope of QR is -3/2.

ST)

Let S(-4, 8) be (x₁, y₁) and T(-1, 10) be (x₂, y₂). Substitute:

$m=\frac{10-8}{-1-(-4)}$

Subtract:

$m=2/3$

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.

Answer 2

Perpendicular     hope this helped