Understanding Parallel and Perpendicular

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/