Answer:
As [tex]m_{1}\neq m_{2}[/tex], we conclude that both lines are not parallel to each other.
Explanation:
We must remember from Analytic Geometry that two lines are parallel to each other if and only if both lines have the same slope. We may calculate each slope by knowing each pair of distinct points passing through each segment:
[tex]m = \frac{y_{B}-y_{A}}{x_{B}-x_{A}}[/tex]
Where:
[tex]m[/tex] - Slope, dimensionless.
[tex]x_{A}[/tex], [tex]x_{B}[/tex] - Initial and final x-Components, dimensionless.
[tex]y_{A}[/tex], [tex]y_{B}[/tex] - Initial and final y-Components, dimensionless.
If we know that [tex]P(x,y) = (3, -5)[/tex], [tex]Q(x, y) = (1, 4)[/tex], [tex]R(x,y) =(-1, 1)[/tex] and [tex]S(x, y) = (3, -3)[/tex], then:
[tex]m_{1} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}}[/tex]
[tex]m_{1} = \frac{4-(-5)}{1-3}[/tex]
[tex]m_{1} = -\frac{9}{2}[/tex]
[tex]m_{2} = \frac{y_{S}-y_{R}}{x_{S}-x_{R}}[/tex]
[tex]m_{2} = \frac{-3-1}{3-(-1)}[/tex]
[tex]m_{2} = -1[/tex]
As [tex]m_{1}\neq m_{2}[/tex], we conclude that both lines are not parallel to each other.
