Writing Equations Of Parallel And Perpendicular Lines Worksheet
Parallel lines have the same slope and will never intersect. Parallel lines continue, literally, forever without touching (assuming that these lines are on the same plane).
Parallel Lines in greater depth
On the other hand, the slope of perpendicular lines are the negative reciprocals of each other, and a pair of these lines intersects at 90 degrees.
Perpendicular Lines in greater depth
Parallel Example
As you can see from the diagram below, these lines:
- have the same slope
- 2
- are never going to intersect
Perpendicular Example
As you can see from the picture below:
- the slope of these lines are negative reciprocals
- $$\frac{2}{3}$$ and $$-\frac{3}{2}$$ are negative reciprocals
- these lines are perpendicular and intersect at 90 degrees
Parallel Lines in Greater Depth
Both of the lines below have the same slope: $$ \frac{1}{2} $$
Therefore these lines are parallel and will never meet.
Problem 1
Are the two lines pictured below parallel?
No.
While these lines may look parallel at first glance, if you look closely and calculate each line's slope, you will find that:
- line 1 has a slope of $$ -\frac{1}{4} $$
- line 2 's slope is $$ - \frac{1}{3} $$
Problem 2
Are the two lines below parallel?
Yes these lines have the same slope, 2, and clearly are never going to intersect.
Perpendicular Lines in Greater Depth
Perpendicular lines:
- intersect at $$ 90^{\circ} $$
- have slopes that are negative reciprocals
Problem 3
Are the two lines in the picture below perpendicular?
Yes
The slope of line 1 is -2 and that of line 2 is $$ \frac{1}{2}$$.
-2 and $$ \frac{1}{2}$$ are negative reciprocals so the lines are perpendicular.
Problem 4
Determine whether or not lines 6 and 5 perpendicular?
Problem 5
Are line P and line L perpendicular?
Writing Equations Of Parallel And Perpendicular Lines Worksheet
Source: https://www.mathwarehouse.com/algebra/linear_equation/parallel-perpendicular-lines.php
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