Worksheets · Pre-Algebra

Translations worksheet for Pre-Algebra

Pre-Algebra translations are done on the coordinate grid: count units left, right, up or down, and give the new coordinates of each vertex. The same slide can be described in words or as a rule like (x - 3, y + 2), and the image points are named with primes, such as A'.

Also taught in Geometry, at its own level and with its own examples.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Translations

Date Period

Translate each point or figure, or describe the translation.

  1. Translate figures or find the rule

    Slide the triangle 5 units right and 5 units down, and draw its image.−10−10−5−551010ABC5
  2. Draw the image under the translation (x,y)→(x+5,y+4).−10−10−5−5551010ABC
  3. Translate by (x,y)→(x−1,y+6).−10−10−5−551010ABC5
  4. Triangle A′B′C′ is a translation of triangle ABC. Write the rule for the translation.−10−10−5−5551010ABCA′B′C′
  5. Translate the triangle 5 units right and 5 units down.−10−10−5−5551010ABC
  6. Draw the image under the translation (x,y)→(x−1,y−5).−10−10−5−5551010ABC
  7. Translate the triangle 4 units left and 3 units down.−10−10−5−5551010ABC
  8. Describe the translation that maps △ABC onto △A′B′C′, as a rule.−10−10−5−5551010ABCA′B′C′
  9. Slide the triangle 2 units right and 5 units up, and draw its image.−10−10−5−5551010ABC
  10. Translate by (x,y)→(x+5,y+4).−10−10−5−5551010ABC

  1. Translate a point

    Translate (−8,0) by the vector ⟨5,6⟩.
  2. Translate (0,−2) 1 unit left and 3 units up.
  3. Translate (−8,11) by the vector ⟨−9,−14⟩.
  4. Translate (−1,8) 1 unit right and 7 units down.
  5. Translate (−3,−1) 1 unit left and 1 unit down.
  6. Translate (−14,14) by the rule (x,y)→(x−15,y−9).
  7. Translate (2,−1) by the vector ⟨1,−2⟩.
  8. Translate (−4,3) 2 units left and 5 units up.
  9. Translate (5,−13) by the vector ⟨12,9⟩.
  10. Translate (−1,−3) by the rule (x,y)→(x−2,y−4).

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

TranslationsAnswer keyVersion 2

Date Period

Translate each point or figure, or describe the translation.

  1. Translate figures or find the rule

    Slide the triangle 5 units right and 5 units down, and draw its image.−10−10−5−51010ABCA′B′C′55(3,−1), (8,−1), (6,2)
  2. Draw the image under the translation (x,y)→(x+5,y+4).−10−10−5−551010ABCA′B′C′5(4,−3),  (6,0),  (2,1)
  3. Translate by (x,y)→(x−1,y+6).−10−10−5−551010ABCA′B′C′5(3,4),  (3,7),  (8,7)
  4. Triangle A′B′C′ is a translation of triangle ABC. Write the rule for the translation.−10−10−5−5551010ABCA′B′C′(x,y)→(x−5,y−5), 5 units left and 5 units down
  5. Translate the triangle 5 units right and 5 units down.−10−10−5−5551010ABCA′B′C′(−2,2),  (2,1),  (4,4)
  6. Draw the image under the translation (x,y)→(x−1,y−5).−10−10−5−5551010ABCA′B′C′(3,2),  (7,3),  (7,0)
  7. Translate the triangle 4 units left and 3 units down.−10−10−5−5551010ABCA′B′C′(−2,−2), (2,−2), (−2,1)
  8. Describe the translation that maps △ABC onto △A′B′C′, as a rule.−10−10−5−5551010ABCA′B′C′(x,y)→(x−5,y−4), 5 units left and 4 units down
  9. Slide the triangle 2 units right and 5 units up, and draw its image.−10−10−5−5551010ABCA′B′C′(−3,3), (−7,3), (−3,−1)
  10. Translate by (x,y)→(x+5,y+4).−10−10−5−5551010ABCA′B′C′(1,−3), (−3,1), (1,0)

  1. Translate a point

    Translate (−8,0) by the vector ⟨5,6⟩.(−3,6)
  2. Translate (0,−2) 1 unit left and 3 units up.(−1,1)
  3. Translate (−8,11) by the vector ⟨−9,−14⟩.(−17,−3)
  4. Translate (−1,8) 1 unit right and 7 units down.(0,1)
  5. Translate (−3,−1) 1 unit left and 1 unit down.(−4,−2)
  6. Translate (−14,14) by the rule (x,y)→(x−15,y−9).(−29,5)
  7. Translate (2,−1) by the vector ⟨1,−2⟩.(3,−3)
  8. Translate (−4,3) 2 units left and 5 units up.(−6,8)
  9. Translate (5,−13) by the vector ⟨12,9⟩.(17,−4)
  10. Translate (−1,−3) by the rule (x,y)→(x−2,y−4).(−3,−7)

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

Translate A(1,2), B(4,2), C(1,5) 3 units left and 2 units down

  1. Left 3 means subtract 3 from x; down 2 means subtract 2 from y.
  2. The rule is (x - 3, y - 2).
  3. Apply it to each vertex.

The answer is (−2,0), (1,0), (−2,3).

Where students go wrong

Mixing up the directions. Left and down mean subtract, right and up mean add, so '3 units left' is x - 3, not x + 3.

Also called translating points, sliding a figure or coordinate translations.

What you can put on this worksheet

On a grid, with the image drawn
Translate the triangle 6 units right and 6 units down. → (2,−3), (7,−3), (4,0)
Translating a point
Translate (3,1) by (x,y)→(x+2,  y+2). → (5,3)
In words, as a vector or as a rule
Translate (1,1) 1 unit right and 5 units down. → (2,−4)
A figure given as a list of vertices
Translate the points 6 units right and 5 units down:
P(0,1), T(−4,7), B(−2,5). List the image of each point. → P′(6,−4), T′(2,2), B′(4,0)
Write the translation rule from the drawing
How far right or left, and up or down, did the figure move? Write the rule. → Translation: (x,y)→(x+4,y+4)

Questions about these worksheets

Yes. Every translations sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Pre-Algebra is usually taken around 7th or 8th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the translations questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: on a grid, with the image drawn, translating a point, in words, as a vector or as a rule, a figure given as a list of vertices and write the translation rule from the drawing. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding the shift to the wrong coordinate. The x part only touches x and the y part only touches y, and swapping them moves the point somewhere else entirely.