Parallel Lines: a and b. Perpendicular Lines: None of the lines are perpendicular.
Practice makes perfect
Two lines are parallel if their slopes are identical. To tell if two lines are perpendicular, we have to check if their slopes are negative reciprocals. Let's tackle these questions one at a time.
Are They Parallel?
For this exercise, we have been given two points on each line, so we have enough information to calculate their slopes using the Slope Formula.
m=y_2- y_1/x_2- x_1
Note that when choosing points to substitute for ( x_1, y_1) and ( x_2, y_2), it does not matter which points on the line you choose, since the result will be the same. Let's start with line a, which passes through ( 0, 4) and ( 4, 3).
We will use a similar method to identify the slopes of lines b and c.
Line
Points
y_2-y_1/x_2-x_1
Slope
a
( 0, 4) & ( 4, 3)
3- 4/4- 0
-1/4
b
( 0, 1) & ( 4, 0)
0- 1/4- 0
-1/4
c
( 2, 0) & ( 4, 4)
4- 0/4- 2
2
Now that we have identified the slope of each line, we can see that a and b have the same slope. Therefore, line a and line b are parallel.
Are They Perpendicular?
For lines with different slopes, we can conclude that they are not parallel. To determine whether or not they are perpendicular, we will calculate the product of their slopes. Any two slopes whose product equals -1 are negative reciprocals, and are therefore perpendicular.
m_1* m_2 ? =-1
Since only line c has a different slope, let's calculate the product of its slope and the slope of a and b.
