Math

QuestionIs rotation a similarity transformation? Answer True or False.

Studdy Solution

STEP 1

Assumptions1. We need to determine whether the statement "Rotation is a similarity transformation" is true or false. . We understand that a similarity transformation, or similar transformation, is a transformation which preserves angles and changes the size of the figure, but not the shape.
3. We understand that a rotation is a transformation that turns a figure about a fixed point, called the center of rotation.

STEP 2

We need to compare the properties of a rotation with those of a similarity transformation.

STEP 3

A rotation preserves the shape of the figure, as it only turns the figure around a fixed point.

STEP 4

A rotation also preserves the size of the figure, as it does not alter the distances between points.

STEP 5

A rotation preserves the angles of the figure, as it does not alter the angles between lines.

STEP 6

Since a rotation preserves the shape, size, and angles of a figure, it meets all the criteria of a similarity transformation.
Therefore, the statement "Rotation is a similarity transformation" is True.

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