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

B. Yes. Their slopes have product -1.

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 = (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 = (3 -(-2))/(2 -(-3))`

`m = (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 = (-6 -(-1))/(15 - 10)`

`m = (-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."