Transformation Composition Worksheet
Explore the composition of geometric transformations including translations, reflections, and rotations on a coordinate plane for Grade 11 math.
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Transformation Composition Worksheet
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Read each question carefully and perform the indicated transformations. Show all your work on the coordinate planes provided.
1. Consider triangle ABC with vertices A(1, 2), B(4, 2), and C(1, 5).
a. Translate the triangle using the rule (x, y) → (x - 5, y + 3). Label the new vertices A'B'C'.
b. Reflect triangle A'B'C' across the x-axis. Label the final vertices A''B''C''.
2. Consider quadrilateral PQRS with vertices P(-2, 1), Q(2, 1), R(2, -2), and S(-2, -2).
a. Rotate the quadrilateral 90° clockwise about the origin. Label the new vertices P'Q'R'S'.
b. Translate quadrilateral P'Q'R'S' using the rule (x, y) → (x + 3, y - 4). Label the final vertices P''Q''R''S''.
3. Which of the following compositions of transformations is equivalent to a single reflection across the y-axis?
Translation (x-2, y) followed by reflection across x=2
Reflection across x=0 followed by reflection across y=0
Rotation 180° about the origin followed by reflection across y=x
Reflection across the x-axis followed by rotation 90° counterclockwise about the origin
4. A composition of two reflections over parallel lines is equivalent to a single .
5. A composition of two reflections over intersecting lines is equivalent to a single .
6. The order in which transformations are composed does not affect the final image.
True
False
7. Describe a sequence of two transformations that maps triangle DEF with vertices D(0, 0), E(3, 0), F(0, 4) to triangle D''E''F'' with vertices D''(-4, -2), E''(-1, -2), F''(-4, 2).