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.