Answer :
The lines L₁ and L₂ are perpendicular to each other.
To determine whether the lines L₁ and L₂ are parallel, perpendicular, or neither, we can use the slope formula.
Find the slope of line L₁ using the points (6, 2) and (8, -2). The slope (m₁) is calculated using the formula:
[tex]m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-2 - 2}{8 - 6} = \frac{-4}{2} = -2[/tex]
So, the slope of L₁ is -2.
Find the slope of line L₂ using the points (5, 1) and (3, 0). The slope (m₂) is calculated using the same formula:
[tex]m_2 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{0 - 1}{3 - 5} = \frac{-1}{-2} = \frac{1}{2}[/tex]
So, the slope of L₂ is [tex]\frac{1}{2}[/tex].
Compare the slopes:
Lines are parallel if their slopes are equal: [tex]m_1 = m_2[/tex]
Lines are perpendicular if the product of their slopes equals -1: [tex]m_1 m_2 = -1[/tex]
Calculate the product of the slopes:
[tex]m_1 m_2 = -2 \times \frac{1}{2} = -1[/tex]
Since [tex]m_1 m_2 = -1[/tex], this indicates that the lines L₁ and L₂ are perpendicular.
