Worksheets · Geometry

Dilations worksheet

A dilation multiplies both coordinates by the scale factor. Bigger than one and the figure grows, between zero and one and it shrinks, and the center stays exactly where it is. It is the only one of the four transformations that changes size rather than just position.

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Sigma Prep · sigmaprep.io/worksheets

Name

Dilations

Date Period

Find the image of each.

  1. Dilate about the origin by a scale factor of 3-10-10-5-55510100ABC
  2. A dilation about the origin sends (−6,4) to (−42,28). Find the scale factor
  3. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  4. A dilation about the origin sends (−5,−4) to (−35,−28). Find the scale factor
  5. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  6. A dilation about the origin sends (3,−6) to (21,−42). Find the scale factor
  7. Dilate about the origin by a scale factor of 3-10-10-5-55510100ABC
  8. A dilation about the origin sends (3,2) to (18,12). Find the scale factor
  9. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  10. A dilation about the origin sends (−3,−6) to (−21,−42). Find the scale factor
  11. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  12. A dilation about the origin sends (9,7) to (63,49). Find the scale factor
  13. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  14. A dilation about the origin sends (−7,2) to (−49,14). Find the scale factor
  15. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  16. A dilation about the origin sends (−2,−3) to (−14,−21). Find the scale factor
  17. Dilate about the origin by a scale factor of 3-10-10-5-55510100ABC
  18. A dilation about the origin sends (3,9) to (21,63). Find the scale factor
  19. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABC
  20. A dilation about the origin sends (8,−3) to (56,−21). Find the scale factor

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

Sigma Prep · sigmaprep.io/worksheets

Name

DilationsAnswer keyVersion 1

Date Period

Find the image of each.

  1. Dilate about the origin by a scale factor of 3-10-10-5-55510100ABCA'B'C'(−3,−3),  (−9,−3),  (−3,−9)
  2. A dilation about the origin sends (−6,4) to (−42,28). Find the scale factor7
  3. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(4,2),  (10,2),  (4,10)
  4. A dilation about the origin sends (−5,−4) to (−35,−28). Find the scale factor7
  5. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(2,−2),  (10,−2),  (2,−10)
  6. A dilation about the origin sends (3,−6) to (21,−42). Find the scale factor7
  7. Dilate about the origin by a scale factor of 3-10-10-5-55510100ABCA'B'C'(3,−3),  (9,−3),  (3,−9)
  8. A dilation about the origin sends (3,2) to (18,12). Find the scale factor6
  9. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(−2,−2),  (−10,−2),  (−2,−10)
  10. A dilation about the origin sends (−3,−6) to (−21,−42). Find the scale factor7
  11. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(6,6),  (10,6),  (6,10)
  12. A dilation about the origin sends (9,7) to (63,49). Find the scale factor7
  13. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(−6,−4),  (−10,−4),  (−6,−10)
  14. A dilation about the origin sends (−7,2) to (−49,14). Find the scale factor7
  15. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(−2,4),  (−10,4),  (−2,10)
  16. A dilation about the origin sends (−2,−3) to (−14,−21). Find the scale factor7
  17. Dilate about the origin by a scale factor of 3-10-10-5-55510100ABCA'B'C'(−3,3),  (−9,3),  (−3,9)
  18. A dilation about the origin sends (3,9) to (21,63). Find the scale factor7
  19. Dilate about the origin by a scale factor of 2-10-10-5-55510100ABCA'B'C'(−2,2),  (−10,2),  (−2,10)
  20. A dilation about the origin sends (8,−3) to (56,−21). Find the scale factor7

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

How to do these

Dilate (3,−4) by a scale factor of 2 about the origin

  1. Multiply both coordinates by 2.
  2. 3 times 2 is 6, and -4 times 2 is -8.

The answer is (6,−8).

Where students go wrong

Adding the scale factor instead of multiplying by it. A dilation by 2 does not move a point two units, it doubles both coordinates. Adding is what a translation does.

Also called dilating a figure, scale factor, enlargement or reduction.

What you can put on this worksheet

On a grid, with the image drawn
Dilate about the origin by a scale factor of 2 → (4,6),  (10,6),  (4,10)
Dilating a point
Dilate (3,1) by a scale factor of 3 about the origin → (9,3)
Dilating a segment
Dilate the segment from (3,1) to (−3,−5) by a scale factor of 2 about the origin. Give the image of the second point → (−6,−10)
Finding the scale factor
A dilation about the origin sends (4,1) to (12,3). Find the scale factor → 3

Questions about these worksheets

Yes. Every dilations 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 dilations 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 4: on a grid, with the image drawn, dilating a point, dilating a segment and finding the scale factor. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding the scale factor instead of multiplying by it. A dilation by 2 does not move a point two units, it doubles both coordinates. Adding is what a translation does.