12-5 Geometric Transformations

Objective

To transform geometric figures using matrix operations

Image Long Description

Matrix T in the Solve It translates the figure. Other transformations dilate, rotate, and reflect such geometric figures.

Essential Understanding You can multiply a 2 × 1 2 times 1  matrix representing a point by a 2 × 2 2 times 2  matrix to rotate the point about the origin or reflect the point across a line.

You can write the n points that define a figure as a 2 × n 2 times n  matrix. For example, you can represent the four vertices of kite ABCD with the 2 × 4 2 times 4  matrix shown.

A B C D x -coordinate y -coordinate [ 5 3 1 3 5 7 5 1 ] table with 2 rows and 1 column , row1 column 1 , table with 1 row and 4 columns , row1 column 1 , eh , column 2 b , column 3 c , column 4 d , end table , row2 column 1 , table with 2 rows and 1 column , row1 column 1 , x . minuscoordinate , row2 column 1 , y . minuscoordinate , end table . matrix with 2 rows and 4 columns , row1 column 1 , 5 , column 2 3 , column 3 1 , column 4 3 , row2 column 1 , 5 , column 2 7 , column 3 5 , column 4 1 , end matrix , end table

A change to a figure is a transformation of the figure. The transformed figure is the image. The original figure is the preimage. In the Solve It, the red figure is the preimage. The blue figure is the image.

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