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College Algebra Exam Review 215

College Algebra Exam Review 215 - 4.3 WHAT ABOUT...

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4.3. WHAT ABOUT REFLECTIONS? 225 also asked to find a formula for the reflection through a plane that does not pass through the origin. A reflection that sends a geometric figure onto itself is a type of sym- metry of the figure. It is not an actual motion that you could perform on a physical model of the figure, but it is an ideal motion. Let’s see how we can bring reflection symmetry into our account of the symmetries of some simple geometric figures. Consider a thickened version of our rectangular card: a rectangular brick. Place the brick with its faces parallel to the coordinate planes and with its centroid at the origin of coordinates. See Figure 4.3.2 . r 2 r 1 r 3 Figure 4.3.2. Rotations and reflections of a brick. The rotational symmetries of the brick are the same as those of the rectangular card. There are four rotational symmetries: the nonmotion
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