Grade 9 Transformation Composition Worksheet

Transformation Composition

Read each question carefully and follow the instructions to perform the transformation compositions. Show all your work for full credit.

1. Triangle ABC has vertices A(1, 2), B(4, 2), and C(2, 5). Translate the triangle by the rule (x, y) → (x - 3, y + 1), then translate the resulting image by the rule (x, y) → (x + 5, y - 4). What are the coordinates of the final image A''B''C''?

2. A point P is located at (3, -2). Reflect point P across the x-axis, then reflect the new point P' across the y-axis. What are the coordinates of the final point P''?

3. Rotate point D(2, 4) 90 degrees clockwise about the origin. Then rotate the resulting point D' 180 degrees counter-clockwise about the origin. What are the coordinates of the final point D''?

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

5. When two reflections are performed over parallel lines, the resulting transformation is a  .

6. The order of transformations in a composition always affects the final image.

7. A rotation of 360 degrees about the origin maps a figure onto itself.

8. Graph the square with vertices E(1,1), F(3,1), G(3,3), H(1,3). Reflect the square across the y-axis, then translate the resulting image E'F'G'H' by the rule (x, y) → (x + 2, y - 1). Plot the final image E''F''G''H'' on the coordinate plane below.