Properties of Orientation & Congruence on a Coordinate Plane

T.i.P.S.

Students must have an understanding of the relationship between the coordinates of the shape before and after its transformation, and the scale factor for a dilation from the origin. Using the coordinates, students are able to identify the scale factor. Students identify the transformation based on given coordinates. Transformations include rotations, reflections, translations, and dilations. Students must be able to make statements about the transformations the figures maintain the same shape, as well as explaining that when the size of the shape is changed proportionally the shapes are no longer congruent, or the exact same. Students must also recognize that the orientation of the figure and/or orientation of the vertices may change depending on the type of movement. These movements of shapes must be on an (x, y) graph.

Example

In the following image, ΔXZY has been transformed to create ΔX'Z'Y'. Explain what type of transformation is represented and what properties of orientation or congruence are demonstrated?

Hint
Possible Solution

TEKS

Supporting Standard 8.10 Two-dimensional shapes. The student applies mathematical process standards to develop transformational geometry concepts. The student is expected to:
(A) generalize the properties of orientation and congruence of rotations, reflections, translations, and dilations of two-dimensional shapes on a coordinate plane

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