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MOTION IN GEOMETRY: TRANSFORMATIONS

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Presentation transcript:

Transformations A transformation is any type of movement in geometry, it can be a change in shape, size, or simply location of an object. The three types of Transformations we will talk about today are Reflections, Rotations and Translations.

Pre-Image And Image Pre-Image is the original figure before any type of transformation takes place. Image is the new figure after the transformation has taken place.

DO YOU SEE MATH IN THIS PICTURE?

What about this one?

How about now?

Vocabulary Isometry: a transformation in which the original figure and it’s image are congruent. Opposite Orientation: when an image appears to be backwards compared to the pre-image.

Reflection A transformation in which a line of reflection acts as a mirror reflecting points from their pre-image to their image.

Reflections A reflection reverses orientation. A reflection is an isometry. A reflection over the x-axis results in a change in the y-coordinate. A reflection in the y-axis results in a change in the x-coordinate.

Which category does it fit?

Which category does it fit?

Which category does it fit?

An isometry is a transformation that does not change the shape or size of a figure. Reflections, translations, and rotations are all isometries. Isometries are also called congruence transformations or rigid motions. Recall that a reflection is a transformation that moves a figure (the preimage) by flipping it across a line. The reflected figure is called the image. A reflection is an isometry, so the image is always congruent to the preimage.

Rotational Symmetry Wind Mill How many degrees can each rotate?

When asked to reflect this graph over the y-axis, this is the graph that was given. Is the student correct?