Honors Geometry Transformations Section 3 Translations and Compositions.

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Presentation transcript:

Honors Geometry Transformations Section 3 Translations and Compositions

A translation (or slide) is a transformation which maps every two points P and Q in the plane to points so that the following properties are true: 1. 2.

The following coordinate notation can define translations in the coordinate plane: (x, y) ( x + a, y + b ) where a and b are constants. This notation shifts the point ________________ and _________. a units to the right b units up

D D

A composition results when two or more transformations are performed one after the other.

Example 1: Sketch the image of after a composition of the given rotation and reflection.

Reflection in the x-axis 90 clockwise about the origin

While the order of the transformations affected the final image in the previous example, that is not the case with a glide reflection. A glide reflection is a composition of a translation and a reflection where the line of reflection is parallel to the direction of the translation.

Example 3: Determine the coordinates of the image of A(4, -2) after the described composition. Is the composition a glide reflection?

Example 4: Determine the coordinates of the image of A(4, -2) after the described composition. Is the composition a glide reflection?