Lesson Objective:

In this lesson, students will learn to...

• Determine if a transformation is isometric and identify corresponding parts of the pre-image and image.

• Identify the type of transformation given a pre-image and an image

Geometric Transformations

The word 'Transformation' means to change. A geometric transformation means making some changes to a geometric shape.

There are two basic groups of transformations:

1. Rigid transformation: the transformation results in NO change in shape or size.

2. Non-rigid transformation: the transformation results in changes in the size but not the shape of the preimage.

Determine if the images shown below display a Rigid or a Non-Rigid Transformation

After a transformation occurs, the original shape of the object is called the Pre-Image and the final shape and position of the object is the Image.

A rigid transformation (also called an isometry) is a transformation that preserves length. This means that both the image and the preimages have the same shape and size. In other words, the images are congruent.

There are three types of rigid transformation:

• Reflections: transformation flips an image across either the x or y-axis

• Translations: transformation that moves a geometric pre-image right, left, up, or down

• Rotations: transformation pivots a pre-image around the origin either clockwise or counter-clockwise?

NOTE: The pre-image and the image under a rigid transformation

• is congruent,

• may orientate differently, (they may not be facing in the same direction)

Non-rigid transformation does not preserve length. So the image can have different shapes or sizes compared to the image.

There is only one(1) type of non-rigid transformation:

• Dilation: transformation enlarges or reduces a pre-image