Topic Review — Shape Transformations

Review Questions

1. Translations Fluency

   1. Translate (4, 7) by right 3, down 5.
   2. Translate (−2, 1) by left 4, up 6.
   3. Translate (0, −3) by right 7, up 2.
   4. Triangle A(1, 2), B(3, 2), C(2, 5) is translated right 2, down 4. Find A′, B′, C′.
   5. Describe the translation that maps (5, 3) to (1, 8).
   6. Describe the translation that maps (−1, −2) to (3, 4).

2. Reflections Fluency

   1. Reflect (5, −3) over the x-axis.
   2. Reflect (−4, 6) over the y-axis.
   3. Reflect (3, 7) over the line y = x.
   4. Reflect (0, −5) over the x-axis.
   5. Triangle P(2, 1), Q(4, 1), R(3, 4) is reflected over the y-axis. Find P′, Q′, R′.
   6. Point A(6, 2) maps to A′(2, 6). What mirror line was used?

3. Rotations Fluency

   1. Rotate (4, 3) by 90° clockwise about the origin.
   2. Rotate (−2, 5) by 90° anticlockwise about the origin.
   3. Rotate (6, −1) by 180° about the origin.
   4. Rotate (3, 0) by 270° clockwise about the origin.
   5. Triangle A(1, 2), B(3, 2), C(2, 5) is rotated 90° CW about the origin. Find A′, B′, C′.
   6. Point P(2, −3) maps to P′(3, 2) after a rotation about the origin. What rotation was applied?

4. Identify the Transformation Understanding

   Identify whether each mapping is a translation, reflection, or rotation. Justify your answer.

   1. A(2, 3) → A′(5, 1); B(4, 3) → B′(7, 1); C(3, 5) → C′(6, 3).
   2. A(1, 4) → A′(1, −4); B(3, 4) → B′(3, −4); C(2, 7) → C′(2, −7).
   3. A(2, 1) → A′(1, −2); B(4, 1) → B′(1, −4); C(3, 3) → C′(3, −3).
   4. Name two properties that are preserved by ALL three transformations studied in this topic.
   5. Which transformation changes the orientation of a shape?

5. Mixed Coordinate Problems Understanding

   1. Point A(3, 4) is reflected over the x-axis to get A′, then A′ is translated right 2, up 1 to get A′′. Find A′′.
   2. Point B(1, 5) is rotated 90° CW to get B′, then reflected over the y-axis to get B′′. Find B′′.
   3. Triangle with vertices (0, 0), (4, 0), (2, 3) is rotated 180° about the origin. List the image vertices.
   4. Image triangle has vertices (−3, 1), (−6, 1), (−4, 4). It was created by reflecting an original triangle over the y-axis. Find the original vertices.

6. Transformation Summary and Reasoning Problem Solving

   1. Complete the table:

      Transformation	Changes position?	Changes orientation?	Changes size/shape?
      Translation	?	?	?
      Reflection	?	?	?
      Rotation	?	?	?

   2. A designer tiles a floor using a single triangle shape and three transformations. Describe how you could use a translation, a reflection, and a rotation to fill a rectangular section of floor with the tile and its transformed images.
   3. Point P(a, b) is rotated 90° CW and then 90° ACW about the origin. What are the final coordinates? Explain why.

7. Successive Transformations Problem Solving

   1. Point A(2, 5) is reflected over the y-axis to get A′, then rotated 90° CW about the origin to get A′′. Find A′′.
   2. Point B(−3, 4) is translated right 5, down 2 to get B′, then reflected over the x-axis to get B′′. Find B′′.
   3. Triangle with vertices (0,0), (3,0), (0,4) is rotated 180° about the origin. List the image vertices and describe what happens to the shape’s orientation.

8. Translation Vectors Understanding

   1. Write the translation vector that maps (2, 3) to (7, 1).
   2. Write the translation vector that maps (−4, 5) to (−1, −2).
   3. A shape is translated by vector (right 3, up 4). What vector would translate it back to the original position?

9. Reflection Lines Understanding

   1. Point (3, −5) is reflected to (−3, −5). What is the mirror line?
   2. Point (4, 2) is reflected to (2, 4). What is the mirror line?
   3. Point (−1, 6) is reflected to (−1, −6). What is the mirror line?
   4. Describe how you can tell which mirror line was used given the original and image coordinates.

10. Congruence and Transformations Fluency

    1. What does it mean for two shapes to be congruent?
    2. Do translations, reflections, and rotations all produce congruent shapes? Explain.
    3. If a shape is congruent to another, does it have to be the same orientation?
    4. True or False: a reflection always changes the orientation of a shape.