8th Grade Math · Dilations Find the scale factor Worksheets
A figure and its image are both drawn. Students work out the scale factor, such as 2 or 1/3.
Make it yours
4 problems · 1 page, plus an answer key
Or print a ready-made one (4 problems · 1 page): worksheet · answer key
How it works: a quick refresher
The rules this worksheet practices, then one problem worked from start to finish.
| To do this | Use this rule |
|---|---|
| Dilate by a scale factor k, centered at the origin | (x, y) → (kx, ky) |
| Enlargement: the image is bigger | k > 1 |
| Reduction: the image is smaller | 0 < k < 1 |
| Find the scale factor | k = image length ÷ original length |
| Scale factor 1/3 | (9, −6) → (3, −2) |
Worked example
Dilate triangle G(3, 6), H(−9, 12), J(−3, −9) by a scale factor of 1/3, centered at the origin.
- 1Multiply both coordinates of every vertex by 1/3, which is the same as dividing by 3.
- 2G(3, 6) becomes G′(1, 2).
- 3H(−9, 12) becomes H′(−3, 4). Keep the negative sign.
- 4J(−3, −9) becomes J′(−1, −3).
- 5The image is one third the size of the original, with the same angles, so the two triangles are similar.
Ready-made versions
Three fixed versions you can link to or share. Each is a PDF with its own answer key.
- Find the scale factor Worksheets, version 1Worksheet PDFAnswer key PDF
- Find the scale factor Worksheets, version 2Worksheet PDFAnswer key PDF
- Find the scale factor Worksheets, version 3Worksheet PDFAnswer key PDF
Grade level and standard
Written for 8th grade math (geometry). It practices what Common Core standard CCSS 8.G.A.3 describes, and also works as review in later grades. How we check standards and answers
Common questions
- Is there an answer key?
- Yes. Every worksheet has a matching answer key with each answer worked on the same grid or layout as the question. The worksheet code printed at the bottom of each page pairs a sheet with its key.
- Is every dilation centered at the origin?
- Yes. Centered at the origin, a dilation multiplies both coordinates by the scale factor, which is the rule 8th grade uses. Dilations about other points come later, in high school geometry.
- How is this different from translations, reflections and rotations?
- Those keep a figure the same size, so the image is congruent. A dilation changes the size but not the shape, so the image is similar. Our transformations worksheets cover the other three.
- Do the answers include fractions?
- Scale factors can be fractions such as 1/2, 1/3 or 3/2, but every vertex is chosen so its image lands on whole-number coordinates.
- How many different versions are there?
- About a million per skill. Each time you press the button the problems are generated fresh, so you can print a different version for every student, a retake, or another night of practice.
- Are the worksheets free?
- Yes. They are free to print and copy for your home or classroom, with no sign-up.
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