By Edwin Bidwell Wilson

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The term Cartesian is used in honor of René Descartes, the seventeenth-century French philosopher and mathematician. The coordinates (x, y) of a point P are referred to as an ordered pair. Q 4 4 3 3 P 2 4 (2, 3) 3 (3, 2) 2 1 (_2, 1) 1 1 (a) 2 3 4 2 (2, 1) 1 x _3 _2 _1 O _1 Figure 3 y y y (3, 0) x _1 _1 1 2 (b) 3 4 _4 _3 _2 _1 _1 (_2, _1) 1 2 (2, _1) (c) 3 x 4 20 Chapter 1 Fundamentals Recall, for example, that (3, 2) and (2, 3) represent different points; that is, the order of the numbers matters.

C) Use the percentage errors you’ve computed as a check on your part (a) answers. Were you correct about which estimate was the most reliable and which was the least? If you missed either one, how might you adjust the reasons or intuitions that you expressed in part (a)? 0 P ( percentage) 1955 F (Fahrenheit temperature) t (year) Figure A Figure B Figure C Global average temperature at Earth’s surface Some correspondences between temperatures on the Celsius and Fahrenheit scales. 5 GRAPHS AND GRAPHING UTILITIES In this section we look at the connection between two basic skills that you’ve worked on in previous courses: • • graphing equations solving equations We also look at these topics in terms of graphing utilities.

C 34. This problem indicates a method for calculating the area of a triangle when the coordinates of the three vertices are given. (a) Calculate the area of ^ABC in the figure. y C(7, 8) B(8, 5) A(3, 4) x A diagram accompanying a proof of the “Pythagorean” theorem in the ancient Chinese text Chou Pei Suan Ching [from Science and Civilisation in China, vol. 3, by Joseph Needham (Cambridge, England: Cambridge University Press, 1959)]. (a) Starting with the right triangle in Figure A, we make four replicas of this triangle and arrange them to form the pattern shown in Figure B.

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