Question

in the graph to the right, are lines l₁ and l₂ perpendicular? explain. choose the correct statement below. a. no, the lines l₁ and l₂ are not perpendicular because the product of their slopes does not equal -1. b. yes, the lines l₁ and l₂ are perpendicular because the product of their slopes equals -1. c. yes, the lines l₁ and l₂ are perpendicular because the product of their slopes does not equal -1. d. no, the lines l₁ and l₂ are not perpendicular because the product of their slopes equals -1. help me solve this view an example get more help clear all final check

Explanation:

Step1: Find slope of \( L_1 \)

Take two points on \( L_1 \), e.g., \( (0, 0) \) and \( (4, 4) \). Slope \( m_1=\frac{4 - 0}{4 - 0}=1 \).

Step2: Find slope of \( L_2 \)

Take two points on \( L_2 \), e.g., \( (0, 0) \) and \( (4, -4) \). Slope \( m_2=\frac{-4 - 0}{4 - 0}=-1 \).

Step3: Check product of slopes

Product \( m_1\times m_2 = 1\times(-1)=-1 \). Perpendicular lines have slope product \( -1 \). So lines are perpendicular.

Answer:

B. Yes, the lines \( L_1 \) and \( L_2 \) are perpendicular because the product of their slopes equals \( -1 \)