Discovering Defining Parts

# Discovering Defining Parts - Discovering Defining Parts of...

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Finding a Defining Vector of a Translation Isometry Discovering Defining Parts of Some Isometries Given a figure and its image under a translation, to find a vector through which the translation is defined: Construct the segment which connects any one point X with its image X' . Let A = X and B = X' . Then, the translation is T AB . In the example below, vertex D is selected as the point X . E' D ' = B C' E D = A C E ' D ' C ' C D E

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θ Finding the Center of Rotation and a Defining Angle of Rotation for a Given Rotation Isometry Given a figure and its image under a rotation, to find the center P of that rotation and its the angle θ : 1) construct segments which connect two points with their images, 2) construct the midpoints and perpendicular bisectors of these two segments, 3) the point where the bisectors intersect is the center P of rotation, 4) for any point A, the angle A P A' is a defining angle of rotation θ . (In the example below, point Y is chosen for the point A.)
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## This note was uploaded on 11/02/2010 for the course MATH modern geo taught by Professor Shirley during the Spring '10 term at University of Texas.

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Discovering Defining Parts - Discovering Defining Parts of...

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