Geometric Transformations Rotations

How many degrees was the figure rotated?

• 90 degrees counterclockwise 

• 180 degrees

• 90 degrees clockwise

Tags

CCSS.HSG.CO.B.6

Translations, reflections and rotations are all known as ________________________.

• Geometry

• Transformations

• Congruent

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.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

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.

Tags

CCSS.8.G.A.3

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.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What is the rule for a 180 degree rotation?

• (-y, -x)

• (y, -x)

• (-x, -y)

• (-y, x)

Answer explanation

A 180 degree rotation moves a figure around two whole quadrants (half a circle across the coordinate plane).
This results in the signs of both the x and y value being "flipped" (opposite) from what it started as.
$\left(x,y\right)\longrightarrow\left(-x,-y\right)$

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What is the rule for a 90 degree counterclockwise rotation?

• (x, y)

• (-y, x)

• (-x, -y)

• (y, -x)

Answer explanation

$\left(x,y\right)\longrightarrow\left(-y,x\right)$

A 90 degree rotation will move a figure around the coordinate plane one quadrant (a quarter of a circle).

This results in the coordinate values switching places and the original y-value changing signs.

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

What type of transformation is this?

• Dilation

• Reflection

• Rotation

• Translation

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5

A turn is also called a ___________.

• Translation

• Reflection

• Rotation

• Transformation

Tags

CCSS.8.G.A.3

CCSS.HSG.CO.A.5