L61 — Translations — Solutions

1. Translating Individual Points

   1. (5, 9) ▶ View Solution
   2. (−2, 3) ▶ View Solution
   3. (6, 2) ▶ View Solution
   4. (3, 2) ▶ View Solution

2. Translating Shapes

   1. A(1,1) B(4,1) C(2,3) right 3, up 2: A′(4,3), B′(7,3), C′(5,5) ▶ View Solution
   2. P(0,0) Q(4,0) R(4,2) S(0,2) left 2, down 3: P′(−2,−3), Q′(2,−3), R′(2,−1), S′(−2,−1) ▶ View Solution
   3. D(−1,2) E(1,2) F(0,5) right 4, down 4: D′(3,−2), E′(5,−2), F′(4,1) ▶ View Solution
   4. J(2,1) K(5,1) L(6,4) M(1,4) left 3, up 1: J′(−1,2), K′(2,2), L′(3,5), M′(−2,5) ▶ View Solution

3. Describing Translations

   1. Right 3, up 3 ▶ View Solution
   2. Left 2, down 4 ▶ View Solution
   3. Left 2, up 4 ▶ View Solution
   4. No horizontal change, up 5 ▶ View Solution

4. Properties of Translations

   1. Side lengths after translation: 3 cm, 4 cm, 5 cm — unchanged; translations preserve size ▶ View Solution
   2. Orientation after translation: No — orientation does not change; shape slides but does not flip or rotate ▶ View Solution
   3. Image overlaps original: False — unless the translation is zero (shape maps to itself) ▶ View Solution
   4. B′ = (7, 4) ▶ View Solution

5. Translation Puzzles

   1. (9, 2) ▶ View Solution
   2. A = (1, 3); B = (4, 3); C = (2, 6) ▶ View Solution
   3. P(1,4) translated twice: Final (2, 0); single equivalent: right 1, down 4 ▶ View Solution
   4. Ship from (2,3): Final position: (4, 7); overall: right 2, up 4 ▶ View Solution

6. Column Vector Notation

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

7. Reverse Translation

   1. A = (4, 2) ▶ View Solution
   2. B = (5, 6) ▶ View Solution
   3. C = (−2, 3) ▶ View Solution
   4. D = (−2, −4) ▶ View Solution

8. Translations on a Coordinate Grid

   1. A(0,0) B(4,0) translated right 3, up 2: A′(3,2), B′(7,2); A′B′ = 4 units = AB; translations preserve length ▶ View Solution
   2. Down 4 (vertical only) ▶ View Solution
   3. Right 3, down 2 — same for all three vertices ▶ View Solution
   4. Right 3, up 3; image vertices: (3,3), (5,3), (5,5), (3,5) ▶ View Solution

9. Combined and Equivalent Translations

   1. Right 3 up 4, then right 2 down 1: Right 5, up 3 ▶ View Solution
   2. Left 6 up 2, then right 4 up 3: Left 2, up 5 ▶ View Solution
   3. Right 5 up 5, then back to start: Left 5, down 5 ▶ View Solution
   4. P(2,3): right 4 up 1, left 7 down 3, right 1 up 2: Final (0, 3); net translation: left 2, no vertical change ▶ View Solution

10. Translations in Context

    1. Chess knight (2,3): right 1 up 2, then right 2 up 1: (5, 6) ▶ View Solution
    2. (8,0), (10,0), (9,2) ▶ View Solution
    3. (13,7), (23,7), (25,14), (11,14) ▶ View Solution
    4. Robot from (0,0): right 4, up 3, left 2, down 5, right 1, up 4: Final: (3, 2); total distance = 19 units ▶ View Solution