Rigid Transformations Practice Problems

Select all the angles of rotation that produce symmetry for this flower. Description:

Flower on polar grid. Grid is made up of 3 circles with the same center. Flower is made up of 4 congruent petals. 2 petals on top half of grid, 2 petals on bottom. Petal length reaches the third outermost circle on the grid.

• 30 degrees

• 45 degrees

• 60 degrees

• 90 degrees

• 120 degrees

Tags

From Unit 1, Lesson 16.

Tags

From Unit 1, Lesson 11.

Translations, rotations, and reflections are three different types of what?

• Transformations

• Geometry

• Vectors

• Shapes

Answer explanation

They are all types of transformations because they transform a figure (position and orientation) on a coordinate plane.

"Sliding" a figure is a _________.

• Translation

• Reflection

• Rotation

• Transformation

Answer explanation

Sliding a figure is a translation, because the figure "slides" on the graph without changing the orientation of the figure.

This transformation takes the geometric figure and "flips" it over a line.

• rotation

• translation

• dilation

• reflection

Answer explanation

"Flipping" a figure over the line results in a reflected version of the figure. This is why we call it a reflection.

The mathematical term for the line that you reflect a shape over is the...

• Mirror

• Reflective tape

• Line that you reflect over

• Line of reflection

Answer explanation

The line that a figure is reflected over is called the line of reflection.

A transformation that “turns” a figure, which one is it?

• rotation

• translation

• reflection

• dilation

Answer explanation

When a figure is turned, this type of movement is called a rotation.

Which type of rotation will not change the orientation of an object?

• 90^o rotation

• 180^o rotation

• 270^o rotation

• 360^o rotation

Answer explanation

360 degree rotation does not change the orientation because it is a full rotation and will result in the figure being back where it started.

All other rotations result in the figure changing orientation.

What two transformations could be happening in this picture? Select all that apply.

• reflection and translation

• rotation and translation

• reflection and rotation

Answer explanation

The figure must be either rotated 180 degrees OR reflected across the y-axis to be oriented the way it is.

Then, a translation would slide the figure into its current position.