Learn

Transformations

There are four basic transformations:

  • Reflection
  • Rotation
  • Translation
  • Dilation

Let’s look at each of the four.

There are four basic transformations:

Reflection is a flip about a line

A rectangle missing a square shape from the top left is reflected over a vertical line. The new image is a rectangle missing a square shape from the top right

A figure is said to have isometry if the figure is the same size after the transformation.

You can explore more with the interactive here.

Rotation

Rotation is a turn about a point

We think of rotations as a turn in degrees. The following is a 90° turn from the pre-image to the image.

The image of an arrow pointing to the right is flipped from the bottom left corner to the top left corner pointing downward

We think of rotations as a turn in degrees. The following is a 180° turn from the pre-image to the image.

The image of an arrow pointing to the right is flipped from the top left corner to the bottom right corner and now faces to the left

We think of rotations as the about of a turn in degrees. The following is a 270° turn from the pre-image to the image.

The image of an arrow pointing to the right is flipped from the top left corner to the bottom left corner pointing upward

The following is a 360° turn from the pre-image to the image, which forms a polygon that will land on itself.

An image of an arrow pointing to the right does not change position

You can explore more with the interactive here.

Just as a polygon can have reflection on itself, a polygon can have a rotation on itself.

Look at these two examples.

Polygons that have symmetry

Remember a reflection is about a line and rotaion is about a point!

Translation

Translation is a slide

The pre-image can slide up or down, left or right, or at a diagonal.

A shaped block is moved from the bottom left to the upper right. The shape remains the same orientation.

Geogebra - Translation

Dilation

Dilation is a figure gets larger or smaller. This will be studied in more detailed later in this course.

A small figure changes into a larger version

You can explore more with the interactive here.

Exercise #1

Identify the transformation

A pentagon shrinks into a smaller pentagon

Answer: dilation

Exercise #2

Identify the transformation

A trapazoid is flipped sideways

Exercise #3

Answer: rotation

Identify the transformation

The upper left corner of a box becomes the upper right corner of a box

Answer: reflection

Exercise #4

Identify the transformation

An arrow pointing to the left is moved several space to the right

 

Answer: translation

Exercise #5

Which transformation does not have isometry?

Answer: dilation

Quilt Patterns

Think about the quilt patterns you found earlier. How might you describe the patterns in this quilt now that you have new vocabulary?

A picture of symmetric flower patterns