Exploring Composition of Transformations in Geometry

What does it mean when we say transformations are not commutative?

• Transformations can only be performed in a specific sequence.

• The order of transformations does not affect the outcome.

• Performing transformations in reverse order yields the same result.

• The order in which transformations are performed can alter the outcome.

In what direction do we read the mathematical notation for compositions of transformations?

• From right to left.

• In any direction.

• From top to bottom.

• From left to right.

What is a glide reflection?

• A reflection followed by a rotation.

• A reflection followed by a translation where the line of reflection is parallel to the direction of the translation.

• A rotation followed by a reflection.

• A translation followed by a dilation.

How can a composition of two translations be simplified?

• By adding the translations together.

• By subtracting one translation from the other.

• By multiplying the translations.

• By dividing one translation by the other.

How can the composition of a reflection and a translation be commutative?

• It is never commutative.

• When the line of reflection is parallel to the direction of the translation.

• When the translation is performed before the reflection.

• When the line of reflection is perpendicular to the direction of the translation.

What results from the composition of two reflections over parallel lines?

• No change to the object.

• A single dilation.

• A single translation.

• A single rotation.

What is the outcome of reflecting an object over the y-axis followed by the x-axis?

• A translation.

• A dilation.

• A rotation of 180 degrees.

• No change to the object.

How can you achieve a single rotation through the composition of rotations?

• By adding the degree measurements of the rotations.

• By dividing one rotation by another.

• By subtracting the degree measurements of the rotations.

• By multiplying the degree measurements of the rotations.

What is the result of a composition of dilations with scale factors of 12 and 1/4?

• A dilation by a scale factor of 1/3.

• A dilation by a scale factor of 12.25.

• A dilation by a scale factor of 48.

• A dilation by a scale factor of 3.

What does a dilation by a negative scale factor represent?

• A rotation followed by a reflection.

• A dilation followed by a translation.

• A reflection followed by a dilation.

• A translation followed by a rotation.