Worksheets · Geometry

Rotations worksheet for Geometry

A quarter turn counterclockwise sends (x, y) to (-y, x), and doing it twice gives the half turn. Everything else follows from repeating that one step. About any other point, shift so that point is the origin, turn, and shift back.

Also taught in Pre-Algebra, at its own level and with its own examples.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Rotations

Date Period

Rotate each point or figure as described.

  1. Rotate on a grid

    Rotate the triangle 90∘ counterclockwise around the origin.−10−10−5−5551010ABC
  2. Rotate 90∘ clockwise about the origin.−10−10−5−5551010ABC
  3. Give the triangle a half turn (180∘) about the origin.−10−10−5−5551010ABC
  4. Rotate the triangle 90∘ clockwise around the origin.−10−10−5−5551010ABC
  5. Rotate 90∘ counterclockwise about the origin.−10−10−5−5551010ABC
  6. Rotate the triangle 180∘ around the origin.−10−10−5−551010ABC5
  7. Rotate 90∘ counterclockwise about the origin.−10−10−5−5551010ABC

  1. Rotate a point counterclockwise about the origin

    Rotate (6,−3) 90∘ counterclockwise about the origin.
  2. Rotate (−8,7) 180∘ about the origin.
  3. Rotate (−8,−5) 90∘ counterclockwise about the origin.
  4. Rotate (3,5) 180∘ about the origin.
  5. Rotate (5,4) 270∘ counterclockwise about the origin.
  6. Rotate (−5,1) 270∘ counterclockwise about the origin.
  7. Rotate (−1,7) 90∘ counterclockwise about the origin.

  1. Rotate a point 90∘90^\circ clockwise, 270∘270^\circ clockwise or 180∘180^\circ about the origin

    Rotate (7,3) 270∘ clockwise about the origin.
  2. Rotate (−4,1) 270∘ clockwise about the origin.
  3. Rotate (−6,−5) 180∘ about the origin.
  4. Rotate (−6,−8) 90∘ clockwise about the origin.
  5. Rotate (2,−5) 90∘ clockwise about the origin.
  6. Rotate (3,−2) 180∘ about the origin.

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

Sigma Prep · sigmaprep.io/worksheets

Name

RotationsAnswer keyVersion 1

Date Period

Rotate each point or figure as described.

  1. Rotate on a grid

    Rotate the triangle 90∘ counterclockwise around the origin.−10−10−5−5551010ABCA′B′C′(−8,−4), (−5,2), (−9,2)
  2. Rotate 90∘ clockwise about the origin.−10−10−5−5551010ABCA′B′C′(4,−7), (5,−4), (7,−8)
  3. Give the triangle a half turn (180∘) about the origin.−10−10−5−5551010ABCA′B′C′(−6,2), (−6,−2), (−9,1)
  4. Rotate the triangle 90∘ clockwise around the origin.−10−10−5−5551010ABCA′B′C′(−3,3), (−3,7), (−8,5)
  5. Rotate 90∘ counterclockwise about the origin.−10−10−5−5551010ABCA′B′C′(4,3),  (9,3),  (6,6)
  6. Rotate the triangle 180∘ around the origin.−10−10−551010ABCA′B′C′−55(2,−5), (−4,−5), (−3,−8)
  7. Rotate 90∘ counterclockwise about the origin.−10−10−5−5551010ABCA′B′C′(2,−5), (8,1), (8,−3)

  1. Rotate a point counterclockwise about the origin

    Rotate (6,−3) 90∘ counterclockwise about the origin.(3,6)
  2. Rotate (−8,7) 180∘ about the origin.(8,−7)
  3. Rotate (−8,−5) 90∘ counterclockwise about the origin.(5,−8)
  4. Rotate (3,5) 180∘ about the origin.(−3,−5)
  5. Rotate (5,4) 270∘ counterclockwise about the origin.(4,−5)
  6. Rotate (−5,1) 270∘ counterclockwise about the origin.(1,5)
  7. Rotate (−1,7) 90∘ counterclockwise about the origin.(−7,−1)

  1. Rotate a point 90∘90^\circ clockwise, 270∘270^\circ clockwise or 180∘180^\circ about the origin

    Rotate (7,3) 270∘ clockwise about the origin.(−3,7)
  2. Rotate (−4,1) 270∘ clockwise about the origin.(−1,−4)
  3. Rotate (−6,−5) 180∘ about the origin.(6,5)
  4. Rotate (−6,−8) 90∘ clockwise about the origin.(−8,6)
  5. Rotate (2,−5) 90∘ clockwise about the origin.(−5,−2)
  6. Rotate (3,−2) 180∘ about the origin.(−3,2)

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

How to do these

Rotate (4,1) 90∘ counterclockwise

  1. Swap the two coordinates.
  2. Then flip the sign of the new x.
  3. So (4, 1) becomes (-1, 4).

The answer is (−1,4).

Where students go wrong

Turning the wrong way. Counterclockwise is the positive direction, so a 90 degree rotation clockwise is the 270 degree one, and doing it by eye lands three quarters out.

Also called rotating points, rotation about the origin or 90 degree rotation.

What you can put on this worksheet

On a grid, with the image drawn
Rotate the triangle 180∘ around the origin. → (−2,2), (−2,7), (3,7)
Rotating about the origin
Rotate (3,1) 180∘ about the origin. → (−3,−1)
Rotate a point about a center
Rotate (1,4) 180∘ about the origin. → (−1,−4)
Clockwise, about the origin
Rotate (1,4) 270∘ clockwise about the origin. → (−4,1)
Rotate a segment or a quadrilateral
Rotate 180∘ about the origin. → (2,−3), (6,−3), (7,−6), (4,−7)
A figure given as a list of vertices, either direction
Rotate the points 90∘ counterclockwise about the origin:
P(0,1), T(−4,7), B(−2,5). List the image of each point. → P′(−1,0), T′(−7,−4), B′(−5,−2)
Name the rotation and write its rule
Name the transformation and write its rule. → Rotation 180∘ about the origin: (x,y)→(−x,−y)

Questions about these worksheets

Yes. Every rotations 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.

Geometry is usually taken around 9th or 10th 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 rotations 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 two 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 7: on a grid, with the image drawn, rotating about the origin, rotate a point about a center, clockwise, about the origin, rotate a segment or a quadrilateral, a figure given as a list of vertices, either direction and name the rotation and write its rule. Tick as many as you want and set how many of each, or let it spread them evenly.

Turning the wrong way. Counterclockwise is the positive direction, so a 90 degree rotation clockwise is the 270 degree one, and doing it by eye lands three quarters out.