Shape Transformations Review — Answers

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1. Translations

   1. (7, 2) ▶ View Solution
   2. (−6, 7) ▶ View Solution
   3. (7, −1) ▶ View Solution
   4. A′(3,−2), B′(5,−2), C′(4,1) ▶ View Solution
   5. Left 4, up 5 ▶ View Solution
   6. Right 4, up 6 ▶ View Solution

2. Reflections

   1. (5, 3) ▶ View Solution
   2. (4, 6) ▶ View Solution
   3. (7, 3) ▶ View Solution
   4. (0, 5) ▶ View Solution
   5. P(2,1) Q(4,1) R(3,4) over y-axis: P′(−2,1), Q′(−4,1), R′(−3,4) ▶ View Solution
   6. y = x (coordinates swapped) ▶ View Solution

3. Rotations

   1. (3, −4) ▶ View Solution
   2. (−5, −2) ▶ View Solution
   3. (−6, 1) ▶ View Solution
   4. (0, 3) ▶ View Solution
   5. A′(2,−1), B′(2,−3), C′(5,−2) ▶ View Solution
   6. 90° anticlockwise ▶ View Solution

4. Identify the Transformation

   1. Translation (right 3, down 2) ▶ View Solution
   2. Reflection over the x-axis ▶ View Solution
   3. 90° clockwise rotation ▶ View Solution
   4. Size (lengths) and shape (angles) ▶ View Solution
   5. Reflection ▶ View Solution

5. Mixed Coordinate Problems

   1. (5, −3) ▶ View Solution
   2. (−5, −1) ▶ View Solution
   3. (0, 0), (−4, 0), (−2, −3) ▶ View Solution
   4. (3, 1), (6, 1), (4, 4) ▶ View Solution

6. Transformation Summary and Reasoning

   1. Translation: Yes / No / No  |  Reflection: Yes / Yes / No  |  Rotation: Yes / No / No ▶ View Solution
   2. Use the original triangle to start one section; translate it right to fill a row; reflect it to create a mirrored copy; rotate 180° to fill remaining gaps — the three transformations together tile the rectangle ▶ View Solution
   3. (a, b) — the two rotations cancel out (90° CW then 90° ACW = 0° net rotation) ▶ View Solution

7. Successive Transformations

   1. A′′ = (5, 2) ▶ View Solution
   2. B′′ = (2, −2) ▶ View Solution
   3. (0, 0), (−3, 0), (0, −4) — orientation is reversed (vertices go in the opposite order) ▶ View Solution

8. Translation Vectors

   1. Right 5, down 2 ▶ View Solution
   2. Right 3, down 7 ▶ View Solution
   3. Left 3, down 4 ▶ View Solution

9. Reflection Lines

   1. y-axis ▶ View Solution
   2. y = x ▶ View Solution
   3. x-axis ▶ View Solution
   4. If only x changes sign: y-axis  |  if only y changes sign: x-axis  |  if x and y are swapped: y = x ▶ View Solution

10. Congruence and Transformations

    1. Same size and shape ▶ View Solution
    2. Yes — all three preserve size and shape (they are isometries) ▶ View Solution
    3. No — congruent shapes can have different orientations (e.g. a reflected image is congruent but flipped) ▶ View Solution
    4. True ▶ View Solution