Answer: The lines L1 and L2 are parallel.
Step-by-step explanation: We are given to determine whether the following lines L1 and L2 passing through the pair of points are parallel, perpendicular or neither :
L1 : (–5, –5), (4, 6),
L2 : (–9, 8), (–18, –3).
We know that a pair of lines are
(i) PARALLEL if the slopes of both the lines are equal.
(II) PERPENDICULAR if the product of the slopes of the lines is -1.
The SLOPE of a straight line passing through the points (a, b) and (c, d) is given by
[tex]m=\dfrac{d-b}{c-a}.[/tex]
So, the slope of line L1 is
[tex]m_1=\dfrac{6-(-5)}{4-(-5)}=\dfrac{6+5}{4+5}=\dfrac{11}{9}[/tex]
and
the slope of line L2 is
[tex]m_2=\dfrac{-3-8}{-18-(-9)}=\dfrac{-11}{-9}=\dfrac{11}{9}.[/tex]
Therefore, we get
[tex]m_1=m_2\\\\\Rightarrow \textup{Slope of line L1}=\textup{Slope of line L2}.[/tex]
Hence, the lines L1 and L2 are parallel.
