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Dilations: Writing the Rule - Printable Math Worksheets year 8 - Wayground

Dilations: Writing the Rule

Marli Jorgensen

Created by Marli Jorgensen

15 questions

8th Grade

Math

Updated Apr 2026

Dilations: Writing the Rule is a Grade 8 mathematics worksheet that helps students connect scale factors to coordinate-rule notation. Across 15 items—8 multiple-choice questions, 3 multiple-select questions, and 4 fill-in-the-blank responses—students classify dilations as enlargements or reductions, identify scale factors greater than or less than 1, and recognize rules in the form (x, y) → (kx, ky). They also distinguish dilations from translations and non-uniform coordinate changes. Students apply these ideas to determine algebraic rules for dilated triangles, quadrilaterals, and other figures, including rules using fractions, decimals, and whole numbers. The fill-in responses provide practice writing rules such as (0.5x,0.5y), (2x,2y), and (2.5x,2.5y) accurately, while the selection questions require students to evaluate several possible transformations at once. This free printable worksheet includes a complete answer key and is suitable for introducing, reinforcing, or checking understanding of writing dilation rules.

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Dilations: Writing the Rule

Total questions: 15

Name
Class
Date
1.
If the scale factor is less than 1, the dilation is...
If the scale factor is less than 1, the dilation is...
a)
an enlargement
b)
a translation
c)
a rotation
d)
a reduction
2.
If the scale factor is greater than 1, the dilation is...
If the scale factor is greater than 1, the dilation is...
a)
an enlargement
b)
a rotation
c)
a translation
d)
a reduction
3.
Enlargement or reduction? Find the scale factor!
Enlargement or reduction?  Find the scale factor!
a)
It's an enlargement; the scale factor is 1/2.
b)
It's an enlargement; the scale factor is 2.
c)
It's a reduction; the scale factor is 1/2.
d)
It's a reduction; the scale factor is 2.
4.

Which of the following algebraic rules represents a dilation? Select all that apply.

a)

(x, y) --> (3x, 3y)

b)

(x, y) --> (3x, 2y)

c)

(x, y) --> (x - 3, y + 5)

d)

(x, y) --> (0.5x, 0.5y)

e)

(x, y) --> (3x, 0.5y)

5.

Which of the following algebraic rules represents a reduction? Select all that apply.

a)

(x, y) --> (3x, 3y)

b)

(x, y) --> (0.5x, 0.5y)

c)

(x, y) --> (0.75x, 0.75y)

d)

(x, y) --> (0.999x, 0.999y)

e)

(x, y) --> (5x, 5y)

6.

Which of the following algebraic rules represents an enlargement? Select all that apply.

a)

(x, y) --> (3x, 3y)

b)

(x, y) --> (0.5x, 0.5y)

c)

(x, y) --> (0.75x, 0.75y)

d)

(x, y) --> (0.999x, 0.999y)

e)

(x, y) --> (5x, 5y)

7.
Figure S is dilated to create Figure T. Which could be the scale factor of the dilation?
Figure S is dilated to create Figure T.  Which could be the scale factor of the dilation?
a)
(x, y)→(2x, 2y)
b)
(x, y)→(1/2 x, 1/2 y)
c)
(x, y)→(3x, 3y)
d)
(x, y)→(4x, 6y)
8.
Write the algebraic rule for the dilation. Don't put any spaces in your answer.

Write the algebraic rule for the dilation. Don't put any spaces in your answer.

(a)  

9.
Quadrilateral WXYZ was dilated with the origin as the center to create quadrilateral W’X’Y’Z’. Which rule best represents…

Quadrilateral WXYZ was dilated with the origin as the center to create quadrilateral W’X’Y’Z’.


Which rule best represents the dilation that was applied to quadrilateral WXYZ to create quadrilateral W’X’Y’Z’?

a)

(x, y) --> (0.4x, 0.4y)

b)

(x, y) --> (x + 3, y + 2)

c)

(x, y) --> (2.5x, 2.5y)

d)

(x, y) --> (x - 3, y - 2)

10.
Triangle A’B’C’ is the dilation of triangle ABC. Which algebraic representation shows this dilation?

Triangle A’B’C’ is the dilation of triangle ABC.


Which algebraic representation shows this dilation?

a)

(x, y) --> (1/2x, 1/2y)

b)

(x, y) --> (2x, 2y)

c)

(x, y) --> (x + 1/2, y)

d)

(x, y) --> (1/2x, y)

11.
Write the algebraic rule for the dilation. Don't put any spaces in your answer.

Write the algebraic rule for the dilation. Don't put any spaces in your answer.

(a)  

12.
Trapezoid A’B’C’D’ is the dilation of trapezoid ABCD. Which algebraic representation shows this dilation?

Trapezoid A’B’C’D’ is the dilation of trapezoid ABCD.


Which algebraic representation shows this dilation?

a)

(x, y) --> (2x, 2y)

b)

(x, y) --> (0.5x, 0.5y)

c)

(2x, 2y) --> (x, y)

d)

(x, y) --> (3x, 2y)

13.
Write an algebraic rule for the dilation. Don't put any spaces in your answer.

Write an algebraic rule for the dilation. Don't put any spaces in your answer.

(a)  

14.
Triangle A’B’C’ is the dilation of triangle ABC. Which algebraic representation shows this dilation?

Triangle A’B’C’ is the dilation of triangle ABC.


Which algebraic representation shows this dilation?

a)

(x, y) --> (1/2x, 1/2y)

b)

(x, y) --> (2x, 2y)

c)

(x, y) --> (x + 1/2, y)

d)

(x, y) --> (1/2x, y)

15.
Write an algebraic rule for the dilation. Don't put any spaces in your answer.

Write an algebraic rule for the dilation. Don't put any spaces in your answer.

(a)  

WaygroundAnswer Key

Dilations: Writing the Rule

Total questions: 15

1.
d) a reduction
2.
a) an enlargement
3.
b) It's an enlargement; the scale factor is 2.
4.
d)

(x, y) --> (0.5x, 0.5y)

, a)

(x, y) --> (3x, 3y)

5.
d)

(x, y) --> (0.999x, 0.999y)

, b)

(x, y) --> (0.5x, 0.5y)

, c)

(x, y) --> (0.75x, 0.75y)

6.
e)

(x, y) --> (5x, 5y)

, a)

(x, y) --> (3x, 3y)

7.
a) (x, y)→(2x, 2y)
8.
(1/2x,1/2y), (.5x,.5y), (0.5x,0.5y)
9.
c)

(x, y) --> (2.5x, 2.5y)

10.
b)

(x, y) --> (2x, 2y)

11.
(2x,2y),
12.
a)

(x, y) --> (2x, 2y)

13.
(2.5x,2.5y), (5/2x,5/2y)
14.
a)

(x, y) --> (1/2x, 1/2y)

15.
(3x,3y)

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FAQs

What does the Dilations: Writing the Rule worksheet cover?

This Grade 8 worksheet builds skill in writing and interpreting coordinate rules for dilations in the form (x, y) → (kx, ky). Its 15 questions ask students to classify scale factors as enlargements or reductions, select valid dilation rules, distinguish uniform scaling from translations or unequal coordinate changes, and write rules using fractions, decimals, and whole numbers.

How can I use this worksheet to teach students to write dilation rules?

Introduce the relationship between the scale factor and the rule (x, y) → (kx, ky), emphasizing that both coordinates use the same multiplier. Then have students classify factors less than 1 and greater than 1 before moving to the worksheet’s multiple-select rule questions and figure-based items; finish with the fill-in responses so they independently write rules such as (0.5x,0.5y) and (2.5x,2.5y).

What mistakes should I watch for on this dilation rules worksheet?

Students may reverse the meaning of the scale factor, calling a factor less than 1 an enlargement or treating a factor greater than 1 as a reduction. They may also accept rules with different multipliers for x and y, confuse a translation such as (x - 3, y + 5) with a dilation, or write the reciprocal rule when identifying which figure was transformed into the image. For fill-in items, check that they multiply both coordinates and enter the rule in the requested no-space format.

How do I assign and grade this dilation worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for all 15 items. Grade printed submissions by scanning student work with the Wayground for Teachers app, or use the digital quiz to review responses online.

How can I differentiate this worksheet for students who need support with writing dilation rules?

Use the worksheet’s Advanced Settings to increase font size or spacing when students need more room to read the coordinate rules and complete the fill-in responses. You can also select a dyslexia-friendly font or translate the worksheet into another language to make the multiple-choice and multiple-select items more accessible.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to support essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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