Sequences of Transformations (Rigid Motions)

Sequences of Transformations (Rigid Motions)

Properties of Sequences of Rigid Motions

• Size and shape stay the same.

• Angle measures stay the same.

• Area and perimeter stay the same.

• Parallel segments or lines stay parallel.

• Pre-image and image are congruent.

Sequences...

Sequences of transformations are performed by doing each transformation in the order listed. Perform the first transformation on the pre-image and each transformation after that on the image created by the previous transformation.

Example

    

The blue trapezoid is translated 4 units right and then reflected over the x-axis to form the red trapezoid.

Example

    

Square ABCD is rotated 90° counterclockwise and then reflected over the y-axis to form square A'B'C'D'.

Example

    

Triangle ABC is rotated 180° about the origin, translated 5 units down, and then reflected over the x-axis to form ∆A'B'C'.

Multiple Choice

What sequence of transformations maps the red parallelogram to the green parallelogram?

• A translation followed by a reflection.

• A rotation followed by a translation.

• A reflection followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

Which sequence could be used to transform hexagon C to hexagon D?

• Translation 4 left and 2 down

• a reflection over the x-axis and a translation 6 units right

• a reflection over the y-axis and a translation 2 units down

• a counter-clockwise rotation of 90 degrees about the origin

Multiple Choice

What sequence of transformations will get you from the blue triangle BCD to the red triangle B"C"D"?

• Rotation, then Rotation

• Rotation, then Dilation

• Reflection, then Rotation

• Translation, then Reflection

Multiple Choice

What sequence of transformations could map triangle ABC to triangle A"B"C"?

• A dilation followed by a rotation.

• A translation followed by a reflection.

• A rotation about the origin followed by a translation.

• A reflection followed by a rotation.

Multiple Choice

Which of the following describes the sequence of transformations shown?

• Reflection followed by a rotation.

• Rotation followed by a translation.

• Reflection across the x-axis followed by a reflection across the y-axis.

• Translation followed by a rotation.