Transformation Composition Worksheet

Transformation Composition

Read each question carefully and show all your work. Apply the given transformations in the order specified.

1. Consider point A(2, 3). Find the coordinates of A'' after the following composition of transformations:

a) Translation T(x+1, y-4)

b) Reflection across the y-axis

A' ( ,  )

A'' ( ,  )

2. Triangle ABC has vertices A(1,1), B(4,1), and C(1,5). Find the vertices of A''B''C'' after a 90° clockwise rotation about the origin followed by a dilation with a scale factor of 2 centered at the origin.

A' ( ,  ), B' ( ,  ), C' ( ,  )

A'' ( ,  ), B'' ( ,  ), C'' ( ,  )

3. Graph the image of rectangle PQRS with vertices P(-4, 4), Q(-1, 4), R(-1, 2), and S(-4, 2) after a reflection across the x-axis followed by a translation (x+5, y-3). Label the initial rectangle PQRS and its final image P''Q''R''S''.

4. The composition of two reflections always results in a rotation.

5. A glide reflection is a composition of a translation and a reflection across a line parallel to the direction of translation.

6. Which sequence of transformations maps triangle ABC to triangle A''B''C''?

7. A   is a transformation that preserves distance and angle measure.

8. The composition of two reflections over parallel lines results in a  .

9. A dilation with a scale factor of 0.5 followed by a translation (x+2, y-1) is an example of a   transformation.

10. Describe a sequence of at least three transformations (translation, reflection, rotation, or dilation) that would map a square in Quadrant I to a congruent square in Quadrant III.