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### Understanding Parallel and Perpendicular

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Date: 03/23/98 at 11:37:31
From: Amanda
Subject: Parallel and perpendicular slopes

Ever since my class started using parallel and perpendicular slopes,
I've been completely lost, and when I ask for help my teacher explains
it in terms that I'm not very familiar with. Help!

- Amanda
```

```
Date: 03/23/98 at 12:57:00
From: Doctor Sam
Subject: Re: Parallel and perpendicular slopes

Amanda,

I'm not sure exactly what is confusing you. I assume that you know
that parallel lines are lines that never intersect. Another way to
say this is that parallel lines "go in the same direction."  Slope is
a mathematical way to talk about the steepness or the direction of a
line, so that is why this topic is coming up now.

Try this. Draw any line whose slope is 2, for example, the line
joining (0,0) to (1,2) has slope 2. Now draw any other line whose
slope is 2. For example, the line connecting (0,3) and (3,6) has
slope 2. You should see that these lines look parallel. What's more,
if you draw any other line parallel to these and then compute its
slope from your graph paper, you will see that it will also have
slope 2.

Parallel lines have the same slope.

Perpendicular lines are a little more complicated. You know that
perpendicular lines intersect at a 90 degree angle. They don't "go in
the same direction." If you were walking along one of the lines you
would have to make a right turn or a left turn in order to move along
a perpendicular line. This change in direction means that the two
lines have different slopes. But the fact that you always make a
90 degree turn means that their slopes are related.

If you draw the line joining (4,0) and (5,2) and then the line joining
(4,0) and (2, 1) you will see that the two lines are perpendicular.
If you compute the slope of each line you will find that the first
line has slope 2 (the rise is 2-0 = 2 and the run is 5-4 = 1).  The
slope of the second line is -1/2 (the "rise" is 0 - 1 = -1  and the
run is 4 - 2 = 2).

The two slopes have opposite signs and their values are reciprocals.
That is (-1/2)(2) = -1.  This is the general pattern of perpendicular
lines: the product of their slopes is always -1.

I hope that helps.

-Doctor Sam,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra

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