Transformation Composition Worksheet

Transformation Composition

Read each question carefully and perform the requested transformations. Show all your work for full credit. Use the provided coordinate planes for graphing.

1. Consider a point A(2, 3). Perform the following composition of transformations:

a. Translate A by the vector < -4, 1 > to get A'.

b. Rotate A' 90° clockwise about the origin to get A''.

What are the coordinates of A''?

2. A triangle with vertices P(1, 1), Q(3, 1), and R(2, 4) is reflected across the y-axis, then reflected across the line y = x. The final coordinates of P'' are  .

3. A square with vertices at (0,0), (2,0), (2,2), and (0,2) undergoes a dilation centered at the origin with a scale factor of 2, followed by a translation of <1, -3>. Which of the following are the new vertices of the square?

4. The composition of two reflections across parallel lines is equivalent to a single translation.

5. Describe a sequence of transformations that would map triangle ABC with vertices A(1,1), B(3,1), C(2,3) to triangle A''B''C'' with vertices A''( -2, 1), B''( -4, 1), C''( -3, 3).