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🔺 8th grade math · Shapes & Space

Slide, flip, turn, stretch

A translation slides every point the same way. Right adds to x, left takes away from x. Up adds to y, down takes away from y. (2, 3) moved 4 right and 1 down is (6, 2).

Worked example

A translation moves every point 1 unit right and 1 unit up. Point P is at (3, 5). What is the x-coordinate of P′?
−6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
Answer: 4
Moving 1 unit right and 1 unit up changes x by 1 and y by 1. P is at (3, 5), so P′ is at (4, 6). The x-coordinate is 4. Answer: 4.

For grown-ups: Transformations: rotations, reflections, translations, dilations; congruence and similarity. Below: three problems to try with the worked answers, and a free printable sheet. Children can practise the same skill as a game, with no sign-up and no ads.

  • CCSS 8.G.A.1–5
What this practises, for teachers

Practices transformations: rotations, reflections, translations, dilations; congruence and similarity (8.G.A.1–5). A printable sheet with its answer key, worked answers on the page, no accounts.

▶ Practise it

For your class

🖨️ Printable sheet and key

On the board with this skill:

Try three

  1. A translation moves every point 2 units right. Point P is at (3, −5). What is the y-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
    Show the answer and how
    Answer: −5
    Moving 2 units right changes x by 2 and y by 0. P is at (3, −5), so P′ is at (5, −5). The y-coordinate is −5. Answer: −5.
  2. A translation moves every point 1 unit left and 1 unit down. Triangle ABC has A at (0, 2), B at (−5, −1) and C at (−3, −5). What is the y-coordinate of B′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyABC
    Show the answer and how
    Answer: −2
    Moving 1 unit left and 1 unit down changes x by −1 and y by −1. B is at (−5, −1), so B′ is at (−6, −2). The y-coordinate is −2. Answer: −2.
  3. A translation moves every point 1 unit left and 4 units down. Point P is at (7, −3). What is the x-coordinate of P′?
    −8−8−6−6−4−4−2−222446688xyP
    Show the answer and how
    Answer: 6
    Moving 1 unit left and 4 units down changes x by −1 and y by −4. P is at (7, −3), so P′ is at (6, −7). The x-coordinate is 6. Answer: 6.

Before and after

Learn first: Angle puzzles and slices (7th)

Comes next: The Pythagorean theorem (8th)

Name: ____________________Date: ____________Score: ____ / 12

Slide, flip, turn, stretch (8th grade)

  1. A translation moves every point 4 units right and 2 units up. Point P is at (0, 3). What is the y-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  2. A translation moves every point 1 unit right. Point P is at (5, 3). What is the y-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  3. A translation moves every point 1 unit right and 2 units up. Point P is at (0, −4). What is the x-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  4. A translation moves every point 3 units right and 3 units up. Point P is at (−3, −3). What is the x-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  5. A translation moves every point 2 units right and 1 unit up. Point P is at (0, −2). What is the y-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  6. A translation moves every point 1 unit right and 1 unit up. Point P is at (−3, 5). What is the x-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  7. A translation moves every point 4 units up. Point P is at (−4, −5). What is the y-coordinate of P′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyP
  8. A translation moves every point 5 units left. Triangle ABC has A at (2, −5), B at (0, 5) and C at (−1, −5). What is the x-coordinate of C′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyABC
  9. A translation moves every point 1 unit left and 2 units up. Triangle ABC has A at (1, −2), B at (5, 2) and C at (0, 4). What is the x-coordinate of B′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyABC
  10. A translation moves every point 1 unit left and 2 units down. Triangle ABC has A at (−5, 0), B at (−2, 4) and C at (3, −3). What is the x-coordinate of C′?
    −6−6−5−5−4−4−3−3−2−2−1−1112233445566xyABC
  11. A translation moves every point 3 units left and 3 units down. Triangle ABC has A at (0, 2), B at (0, 7) and C at (7, 7). What is the x-coordinate of C′?
    −8−8−6−6−4−4−2−222446688xyABC
  12. A translation moves every point 1 unit right. Point P is at (−2, −3). What is the y-coordinate of P′?
    −8−8−6−6−4−4−2−222446688xyP

Answer key

  1. 5
  2. 3
  3. 1
  4. 0
  5. −1
  6. −2
  7. −1
  8. −6
  9. 4
  10. 2
  11. 4
  12. −3

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