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Transformation of Graphs Using Matrices - Dilation

A type of transformation that occurs when a figure is enlarged or reduced, the transformation is called a dilation . A dilation requires a center point and a scale factor . You can use scalar multiplication to perform dilations in matrices.

Example:

Write the vertex matrix for Δ A B C with A ( 2 , 1 ) , B ( 1 , 3 ) , and C ( 3 , 2 ) . Then find the coordinates of the vertices of Δ A ' B ' C ' after a dilation by a scale factor of 2 .

[ 2 1 3 1 3 2 ]

The scale factor is 2 . So, multiply the vertex matrix by the scale factor of 2 .

2 [ 2 1 3 1 3 2 ] = [ 4 2 6 2 6 4 ]

The coordinates of the vertices of Δ A ' B ' C ' are A ' ( 4 , 2 ) , B ' ( 2 , 6 ) , and C ' ( 6 , 4 ) .