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Unformatted text preview: x 1 ,y 1 ) and ( x 2 ,y 2 ), then we can introduce the point R which shares its last coordinate with P and its rst with Q that is, R has coordinates ( x 2 ,y 1 ) (see Figure 1.3 ); then the triangle with vertices P , Q , and R has a right angle at R . Thus, the line segment PQ is the hypotenuse, whose length | PQ | is related to the lengths of the legs by Pythagoras Theorem | PQ | 2 = | PR | 2 + | RQ | 2 . But the legs are parallel to the axes, so it is easy to see that | PR | = | x | = | x 2 x 1 | | RQ | = | y | = | y 2 y 1 | and the distance from P to Q is related to their coordinates by | PQ | = r x 2 + y 2 = r ( x 2 x 1 ) 2 + ( y 2 y 1 ) 2 . (1.1) 1 We shall explore some of the diFerences between rectangular and oblique coordinates in Exercise 14 ....
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.
- Fall '08