Question

Is the line through points P(–3, –2) and Q(2, 3) perpendicular to the line through points R(10, –1) and S(15, –6)? Explain.

Answer 1

Answer:

B. Yes. Their slopes have product -1.

Step-by-step explanation:

Given:

Line passing through P(-3, -2) and Q(2, 3)

Line passing through R(10, -1) and S(15, -6)

Required:

To determine if both lines are perpendicular.

SOLUTION:

Two lines are considered perpendicular if the product of their slopes equal -1.

To determine if both lines given in the question are perpendicular, first, calculate their slope using: $m = \frac{y_2 - y_1}{x_2 - x_1}$

Slope of line passing through P(-3, -2) and Q(2, 3):

Let,

$P(-3, -2) = (x_1, y_1)$

$Q(2, 3) = (x_2, y_2)$

$m = \frac{3 -(-2)}{2 -(-3)}$

$m = \frac{5}{5} = 1$

Slope of line passing through R(10, -1) and S(15, -6):

Let,

$R(10, -1) = (x_1, y_1)$

$S(15, -6) = (x_2, y_2)$

$m = \frac{-6 -(-1)}{15 - 10}$

$m = \frac{-5}{5} = -1$

The product of their slopes = 1 × -1 = -1

Therefore, the lines are perpendicular.

The answer is: B. "Yes. Their slopes have product -1."