Stitz-Zeager_College_Algebra_e-book

If a point other than the origin happens to lie on

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Unformatted text preview: point other than the origin happens to lie on the axes, we typically refer to the point as lying on the positive or negative x-axis (if y = 0) or on the positive or negative y -axis (if x = 0). For example, (0, 4) lies on the positive y -axis whereas (−117, 0) lies on the negative x-axis. Such points do not belong to any of the four quadrants. One of the most important concepts in all of mathematics is symmetry.5 There are many types of symmetry in mathematics, but three of them can be discussed easily using Cartesian Coordinates. Definition 1.1. Two points (a, b) and (c, d) in the plane are said to be • symmetric about the x-axis if a = c and b = −d • symmetric about the y -axis if a = −c and b = d • symmetric about the origin if a = −c and b = −d 5 According to Carl. Jeff thinks symmetry is overrated. 1.1 The Cartesian Coordinate Plane 5 Schematically, y Q(−x, y ) P (x, y ) 0 x R(−x, −y ) S (x, −y ) In the above figure, P and S are symmetric about the x-axis, as are Q and R; P and Q are symmetric about the y -axis, as are R and S ; and P and R are symmetric about the...
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This note was uploaded on 05/03/2013 for the course MATH Algebra taught by Professor Wong during the Fall '13 term at Chicago Academy High School.

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