G.3: Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).

Coordinate and transformational geometry. The student uses the process skills to generate and describe rigid transformations (translation, reflection, and rotation) and non-rigid transformations (dilations that preserve similarity and reductions and enlargements that do not preserve similarity).

G.3.ADescribe and perform transformations of figures in a plane using coordinate notation.G.3.BDetermine the image or pre-image of a given two-dimensional figure under a composition of rigid transformations, a composition of non-rigid transformations, and a composition of both, including dilations where the center can be any point in the plane.G.3.CIdentify the sequence of transformations that will carry a given pre-image onto an image on and off the coordinate plane.G.3.DIdentify and distinguish between reflectional and rotational symmetry in a plane figure.
Example Problems
A sequence of transformations is described below.
1. A reflection over a line

2. A dilation about the point P
What must be preserved under this sequence of transformations:
angle measures and/or segment lengths?
A sequence of transformations is described below.
1. A translation
2. A rotation about a point A
3. A reflection over a line

What must be preserved under this sequence of transformations:
angle measures and/or segment lengths?
A sequence of transformations is described below.
1. A rotation about a
point S
2. A dilation about the same
point S
What must be preserved under this sequence of transformations:
angle measures and/or segment lengths?
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