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Perform each of the following: i. Show that two distinct reflections 2, and 2, commute if and only if m 1 l. ii. Let P be any point. Prove that the half-turn about P is given by H„x=-x+2P for all xe E. iii. Show that the product of two distinct half-turns is a translation along the line joining their centers.

Perform each of the following: i. Show that two distinct reflections 2, and 2, commute if and only if m 1 l. ii. Let P be any point. Prove that the half-turn about P is given by H„x=-x+2P for all xe E. iii. Show that the product of two distinct half-turns is a translation along the line joining their centers.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 29E
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1. Perform each of the following: i. Show that two distinct reflections 2, and Q, commute if and only if m 1 l . ii. Let P be any point. Prove that the half-turn about P is given by Hx=-x+2P for all xe E. ST 111. Show that the product of two distinct half-turns is a translation along the line joining their centers.
Transcribed Image Text:1. Perform each of the following: i. Show that two distinct reflections 2, and Q, commute if and only if m 1 l . ii. Let P be any point. Prove that the half-turn about P is given by Hx=-x+2P for all xe E. ST 111. Show that the product of two distinct half-turns is a translation along the line joining their centers.
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