Question

Determine whether lines L1 and L2 passing through the pairs of points are parallel, perpendicular, or neither. L1 : (–5, –5), (4, 6) L2 : (–9, 8), (–18, –3)

Answer 1

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

$m=\dfrac{d-b}{c-a}.$

So, the slope of line L1 is

$m_1=\dfrac{6-(-5)}{4-(-5)}=\dfrac{6+5}{4+5}=\dfrac{11}{9}$

and

the slope of line L2 is

$m_2=\dfrac{-3-8}{-18-(-9)}=\dfrac{-11}{-9}=\dfrac{11}{9}.$

Therefore, we get

$m_1=m_2\\\\\Rightarrow \textup{Slope of line L1}=\textup{Slope of line L2}.$

Hence, the lines L1 and L2 are parallel.