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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,
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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