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Transformation in Transformation in GeometryGeometry

Lesson 9Lesson 9

Aim:Aim: Identifying and Identifying and describing transformationdescribing transformationFor this lesson we will:For this lesson we will: Rotate a geometric figure.Rotate a geometric figure. Reflect a figure over a line of Reflect a figure over a line of

symmetry.symmetry. Translate a figure by sliding it to a Translate a figure by sliding it to a

different location.different location. Use dilation by enlarging or reducing Use dilation by enlarging or reducing

the size of a figure without changing the size of a figure without changing its form or shape.its form or shape.

Transformation

A rule for moving every point in a plane figure to a new location.

Translation

A transformation that moves each point in a figure the same distance in the same direction.

• In a translation a figure slides up or down, or left or right. No change in shape or size. The location changes.

• In graphing translation, all x and y coordinates of a translated figure change by adding or subtracting.

Reflection

A transformation where a figure is flipped across a line such as the x-axis or the y-axis.

• In a reflection, a mirror image of the figure is formed across a line called a line of symmetry. No change in size. The orientation of the shape changes. In graphing, a reflection across the x -axis changes the sign of the y coordinate. A reflection across the y-axis changes the sign of the x-coordinate.

Rotation

A transformation where a figure turns about a fixed point without changing its size and shape.

– In a rotation, figure turns around a fixed point, such as the origin. No change in shape, but the orientation and location change.

– Rules for rotating a figure about the origin in graphing.

– Rules for 90 degrees rotation- Switch the coordination of each point. Then change the sign of the y coordinate. Ex. A (2,1) to A’ ( 1,-2)

Dilation

A transformation where a figure changes size.

Dilation• In dilation, a figure is enlarged or

reduced proportionally. No change in shape, but unlike other transformation, the size changes.

• In graphing, for dilation, all coordinates are divided or multiplied by the same number to find the coordinates of the image.