Answer:
Perpendicular
Step-by-step explanation:
Given
[tex]Line\ 1: (2, -3), (-4, -6)[/tex]
[tex]Line\ 2: (-3, 2), (2, -8)[/tex]
Required
Tell the relationship between both lines
We start by calculating the slopes (m) of both lines.
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
For Line 1:
[tex]m_1 = \frac{-6 - (-3)}{-4 - 2}[/tex]
[tex]m_1 = \frac{-6 +3}{-4 - 2}[/tex]
[tex]m_1 = \frac{-3}{-6}[/tex]
[tex]m_1 = \frac{1}{2}[/tex]
For Line 2:
[tex]m_2 = \frac{-8 - 2}{2 - (-3)}[/tex]
[tex]m_2 = \frac{-8 - 2}{2 +3}[/tex]
[tex]m_2 = \frac{-10}{5}[/tex]
[tex]m_2 = -2[/tex]
The lines are not parallel because [tex]m_1 \ne m_2[/tex]
However, they are perpendicular, because:
[tex]m_1 = -\frac{1}{m_2}[/tex]
To prove this, substitute values for m1 and m2
[tex]\frac{1}{2} = -\frac{1}{-2}[/tex]
[tex]\frac{1}{2} = \frac{1}{2}[/tex] --- Proved
