Question

What do you recall about transformations in a plane? What is important to remember about transformations? What's the difference between rigid transformations and nonrigid transformations?

Answer 1

1)

Any image in a plane could be altered by using different operations, or transformations. Here are the most common types:

• Translation is when we slide a figure in any direction.

• Reflection is when we flip a figure over a line.

• Rotation is when we rotate a figure a certain degree around a point.

• Dilation is when we enlarge or reduce a figure.

2)

Transformations map one set of points onto another set of points, generally with the purpose of changing the position, size, and/or shape of the figure made up by the first set of points. The first set of points, from the domain of the transformation, is called the set of pre-images, whereas the second set of points, from the range of the transformation, is called the set of images. Therefore, a transformation maps each pre-image point to its image point.

3)

• A rigid transformation (also called an isometry) is a transformation of the plane that preserves length.

Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".

• non-rigid transformations that change the size but not the shape of the preimage.

example is dilation.