Worksheets · Geometry

Dilations worksheet

A dilation about the origin multiplies both coordinates by the scale factor; about any other center, it multiplies the distance from that center. 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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Name

Dilations

Date Period

Answer each question.

  1. Dilate a figure on a grid

    Dilate the quadrilateral about the origin by a scale factor of 2.−10−10−5−5551010ABCD
  2. Graph the image of △ABC after a dilation by 32 centered at (−5,−6).−10−10−5−5551010ABC
  3. Graph the image after a dilation of scale factor 3 about (0,0).−10−10−5−5551010ABC
  4. Graph quadrilateral ABCD dilated by 12 about (0,0).−10−10−5−5551010ABCD
  5. Dilate the triangle by a factor of 13, with the origin as the center.−10−10−5−5551010ABC

  1. Find the scale factor

    A triangle with sides 10, 10, 12 is dilated to a triangle with sides 20, 20, 24. Find the scale factor.
  2. A 8 by 16 rectangle is dilated to a 6 by 12 rectangle. Find the scale factor.
  3. A square with perimeter 28 units is dilated to a square with perimeter 84 units. Find the scale factor.
  4. A circle with radius 8 units is dilated to a circle with radius 2 units. Find the scale factor.
  5. A dilation about the origin sends (−3,6) to (−2,4). Find the scale factor.

  1. Dilate about a center other than the origin

    Segment AB has A(−4,−2) and B(2,−5). Dilate it by a scale factor of 23 about (2,−2). Give the images of A and B.
  2. A dilation with scale factor 3 sends (−5,−4) to (−9,−6). Find the center of the dilation.
  3. A dilation centered at (−4,0) with scale factor 2 sends a point to (0,−2). Find the point.
  4. Dilate (1,−5) by a scale factor of 12 about (−3,−3).
  5. The image of (3,5) under a dilation centered at (2,1) is (6,17). Find the scale factor.

  1. Classify dilations and find lengths

    A segment 10 units long is dilated, and its image is 5 units long. Find the scale factor. Is the dilation an enlargement or a reduction?
  2. A triangle with a perimeter of 18 units is dilated by a scale factor of 23. Is it an enlargement or a reduction? What is the image's perimeter?
  3. A segment 3 units long is dilated by a scale factor of 3. Is it an enlargement or a reduction? How long is the image?
  4. A rectangle 2 units by 4 units is dilated by a scale factor of 52. Is it an enlargement or a reduction? What are the image's dimensions?
  5. After a dilation by a scale factor of 13, the image of a segment is 5 units long. Is the dilation an enlargement or a reduction? How long was the segment?

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

Sigma Prep · sigmaprep.io/worksheets

Name

DilationsAnswer keyVersion 1

Date Period

Answer each question.

  1. Dilate a figure on a grid

    Dilate the quadrilateral about the origin by a scale factor of 2.−10−10−5−5551010ABCDA′B′C′D′(−8,−4), (−6,−8), (6,2), (−8,4)
  2. Graph the image of △ABC after a dilation by 32 centered at (−5,−6).−10−10−5−5551010ABCA′B′C′(7,6),  (1,6),  (7,9)
  3. Graph the image after a dilation of scale factor 3 about (0,0).−10−10−5−5551010ABCA′B′C′(6,−9), (−3,−9), (6,−3)
  4. Graph quadrilateral ABCD dilated by 12 about (0,0).−10−10−5−5551010ABCDA′B′C′D′(−4,−4), (3,−2), (3,2), (−2,4)
  5. Dilate the triangle by a factor of 13, with the origin as the center.−10−10−5−5551010ABCA′B′C′(3,2), (1,−3), (3,−2)

  1. Find the scale factor

    A triangle with sides 10, 10, 12 is dilated to a triangle with sides 20, 20, 24. Find the scale factor.2
  2. A 8 by 16 rectangle is dilated to a 6 by 12 rectangle. Find the scale factor.34
  3. A square with perimeter 28 units is dilated to a square with perimeter 84 units. Find the scale factor.3
  4. A circle with radius 8 units is dilated to a circle with radius 2 units. Find the scale factor.14
  5. A dilation about the origin sends (−3,6) to (−2,4). Find the scale factor.23

  1. Dilate about a center other than the origin

    Segment AB has A(−4,−2) and B(2,−5). Dilate it by a scale factor of 23 about (2,−2). Give the images of A and B.(−2,−2) and (2,−4)
  2. A dilation with scale factor 3 sends (−5,−4) to (−9,−6). Find the center of the dilation.(−3,−3)
  3. A dilation centered at (−4,0) with scale factor 2 sends a point to (0,−2). Find the point.(−2,−1)
  4. Dilate (1,−5) by a scale factor of 12 about (−3,−3).(−1,−4)
  5. The image of (3,5) under a dilation centered at (2,1) is (6,17). Find the scale factor.4

  1. Classify dilations and find lengths

    A segment 10 units long is dilated, and its image is 5 units long. Find the scale factor. Is the dilation an enlargement or a reduction?12, reduction
  2. A triangle with a perimeter of 18 units is dilated by a scale factor of 23. Is it an enlargement or a reduction? What is the image's perimeter?Reduction, 12
  3. A segment 3 units long is dilated by a scale factor of 3. Is it an enlargement or a reduction? How long is the image?Enlargement, 9
  4. A rectangle 2 units by 4 units is dilated by a scale factor of 52. Is it an enlargement or a reduction? What are the image's dimensions?Enlargement, 5 by 10
  5. After a dilation by a scale factor of 13, the image of a segment is 5 units long. Is the dilation an enlargement or a reduction? How long was the segment?Reduction, 15

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, enlargement or reduction.

What you can put on this worksheet

On a grid, with the image drawn
Draw the image of ABCD after a dilation by 12 about the origin. → (−4,−1), (4,−1), (2,3), (−1,3)
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 circle with radius 9 units is dilated to a circle with radius 36 units. Find the scale factor. → 4
About a point other than the origin
A dilation with scale factor 4 sends (0,1) to (−9,19). Find the center of the dilation. → (3,−5)
Enlargement or reduction
A triangle with a perimeter of 6 units is dilated by a scale factor of 2. Is it an enlargement or a reduction? What is the image's perimeter? → Enlargement, 12

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 6: on a grid, with the image drawn, dilating a point, dilating a segment, finding the scale factor, about a point other than the origin and enlargement or reduction. 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.