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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 Fall '08
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 Calculus, Cartesian Coordinate System, Descartes, Rectangular Coordinates, oblique coordinates, respective rectangular coordinates

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