Question

Line Equation
Line A y=−12x−2

Line B y=2x−3

Line C y=12x+2

Line D y=2x+5




(1 point)
Responses

Line A is perpendicular to Line B
Line A is perpendicular to Line B

Line A is perpendicular to Line C
Line A is perpendicular to Line C

Line C is perpendicular to Line D
Line C is perpendicular to Line D

Line B is perpendicular to Line D

Answer 1

To determine if two lines are perpendicular, we can use the slopes of the lines from their equations in the form \( y = mx + b \), where \( m \) is the slope. Two lines are perpendicular if the product of their slopes is -1.

Let's identify the slopes of each line:

- Line A: \( y = -12x - 2 \) → slope \( m_A = -12 \)
- Line B: \( y = 2x - 3 \) → slope \( m_B = 2 \)
- Line C: \( y = 12x + 2 \) → slope \( m_C = 12 \)
- Line D: \( y = 2x + 5 \) → slope \( m_D = 2 \)

Now we can check for perpendicularity:

1. **Line A and Line B**: \( m_A \times m_B = -12 \times 2 = -24 \) (not perpendicular)
2. **Line A and Line C**: \( m_A \times m_C = -12 \times 12 = -144 \) (not perpendicular)
3. **Line C and Line D**: \( m_C \times m_D = 12 \times 2 = 24 \) (not perpendicular)
4. **Line B and Line D**: \( m_B \times m_D = 2 \times 2 = 4 \) (not perpendicular)

None of the line pairs here are perpendicular.

Therefore, the correct response is that **none of the given pairs of lines are perpendicular**.