Stitz-Zeager_College_Algebra_e-book

# Example 112 let p be the point 2 3 find the points

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Unformatted text preview: origin, as are Q and S . Example 1.1.2. Let P be the point (−2, 3). Find the points which are symmetric to P about the: 1. x-axis 2. y -axis 3. origin Check your answer by graphing. Solution. The ﬁgure after Deﬁnition 1.1 gives us a good way to think about ﬁnding symmetric points in terms of taking the opposites of the x- and/or y -coordinates of P (−2, 3). 1. To ﬁnd the point symmetric about the x-axis, we replace the y -coordinate with its opposite to get (−2, −3). 2. To ﬁnd the point symmetric about the y -axis, we replace the x-coordinate with its opposite to get (2, 3). 3. To ﬁnd the point symmetric about the origin, we replace the x- and y -coordinates with their opposites to get (2, −3). y 3 P (−2, 3) (2, 3) 2 1 −3 −2 −1 −1 1 2 3 −2 −3 (−2, −3) (2, −3) x 6 Relations and Functions One way to visualize the processes in the previous example is with the concept of reﬂections. If we start with our point (−2, 3) and pretend the x-axis is a mirror, then the reﬂection of (−2, 3) across the x-axis would lie at (−2, −3). If we...
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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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