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Lecture 11: Slopes and Right Angles
June 16, 2010
We now introduce the idea of the
slope of a segment.
The slope is always measured relative to a
given coordinate system, but as long as we have only one coordinate system at hand, there is no
reason to keep on mentioning it.
Defnition.
If
AC
is a segment and
A
= (
a, b
) and
C
= (
c, d
), then
the slope of
AC
is
d
−
b
c
−
a
.
This is the familiar “rise over the run.” Notice that a vertical segment does not have a slope.
The segment
AC
has the same slope as the segment
CA
. It does not matter in what order the
endpoints are given.
Comment.
It is true that any two segments that are contained in the same line have the same
slope; we shall return to this important fact later. Unlike the deFnition of the slope of a segment,
this fact is NOT a mere matter of deFnition. It is a wonderful consequence of the deFnition of the
slope of a segment and the properties of the cartesian coordinate system.
Fact 1.
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This note was uploaded on 11/23/2011 for the course MATH 6302 taught by Professor Madden during the Summer '11 term at LSU.
 Summer '11
 MADDEN
 Math, Angles, Slope

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