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PARALLEL AND PERPENDICULAR LINES
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Two lines in a plane are parallel if they never intersect; they have the same "slant".
SLOPES OF PARALLEL LINES:
Two lines are parallel
(
∥
)
if and only if:
- they are both vertical; OR
- they have the same slope.
|
Two lines are perpendicular if they intersect at a 90° angle. For example, the x-axis and
y-axis are perpendicular.
SLOPES OF PERPENDICULAR LINES:
Suppose two lines have slopes
m
1
and
m
2
.
These lines are perpendicular
(
⊥
)
if and only if
m
1
=
-
1
m
2
; i.e.,
the slopes are opposite reciprocals.
|
Equivalently, two lines are perpendicular if and only if their slopes multiply to -1 .
For example, lines with slopes 2
and -
1
2
are perpendicular.
It is easy to see that this is the correct characterization for perpendicular lines, by studying
the sketch below.
The yellow triangle, with base of length 1 and right side of length m ,
shows that the slope of the first line is riserun
=m
1=m .
Now, imagine that this yellow triangle is a block of wood that is glued to the line.
Rotate this block of wood counter-clockwise by
90° (so that the original base is now vertical).
Using the rotated triangle to compute the slope of the new, rotated, line gives:
riserun
=1
-m=-
1m
.
Easy! Voila!
On this exercise, you will not key in your answer.
However, you can check to see if your answer is correct.