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• Printable Scale Factor Worksheets in PDF: Dilation Practice with Answers

Printable Scale Factor Worksheets in PDF: Dilation Practice with Answers

Scale factor tells you how much a figure has been enlarged or reduced, using the formula scale factor = new dimension ÷ original dimension. These free grade 7 worksheets give students practice finding scale factor and applying it to dilations, and every printable PDF includes a full answer key. For more geometry practice, see Brighterly’s Geometry Worksheets collection.

Scale Factor Worksheets: Free Download

This topic is available as one downloadable worksheet file:

Worked Scale Factor Examples

Example 1: Finding the Scale Factor

A rectangle with sides 4 cm and 6 cm is enlarged to a similar rectangle with sides 8 cm and 12 cm.

Scale factor = new dimension ÷ original dimension = 8 ÷ 4 = 2 (checking with the other side: 12 ÷ 6 = 2, which matches).

So the scale factor is 2 — the new rectangle is exactly twice the size of the original.

Example 2: Dilating a Triangle

A triangle has vertices at (1, 1), (3, 1), and (3, 4). To dilate it by a scale factor of 2 from the origin, multiply each coordinate by 2:

• (1, 1) → (2, 2)
• (3, 1) → (6, 2)
• (3, 4) → (6, 8)

The new triangle is the same shape as the original, just twice as large and twice as far from the origin.

More Geometry Worksheets

• Similar Triangles Worksheets
• Area and Perimeter Worksheets
• Identifying Shapes Worksheets
• Area of Composite Figures Worksheets (Grade 6th)
• Area of Right Triangle Worksheet
• Pairs Of Angles Worksheets
• Quadrilateral Worksheets

To check overall progress, try Brighterly’s 7th grade math test, or explore this special full 7th Grade Math Worksheets collection.

Skills Practiced with These Scale Factor Worksheets

• Calculating proportional ratios
• Comparing similar figures
• Solving for missing dimensions
• Converting between measurement units
• Recognizing enlargement and reduction

As the worksheets progress, they start with simpler problems and gradually move to more challenging ones — a scaffolded structure that helps students build proportional reasoning skills step by step rather than jumping straight into complex dilations.

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Scale Factor Worksheets: FAQ

How do I explain scale factor to a child?

You can explain scale factor to a child like the zoom button on a camera. If the scale factor is greater than 1, the shape grows bigger, just like zooming in. If the scale factor is less than 1, the shape shrinks, just like zooming out. This simple comparison helps kids connect an abstract number to something they already understand.

How do you find a scale factor?

To find a scale factor, compare two similar shapes by dividing a side length on the new figure by the matching side length on the original figure. As long as the two figures are truly similar, this ratio will be the same no matter which pair of matching sides you use, which is a useful way to double-check your answer.

Do these worksheets include an answer key?

Yes, every worksheet in this set includes a full answer key, so students can check whether they found the correct scale factor or dilated a figure correctly. This lets them catch mistakes right away and build confidence working through proportional reasoning problems on their own, without needing a teacher to check each answer.

What other worksheets pair well with scale factor practice?

This worksheet pairs well with Brighterly’s wider geometry cluster, including similar triangles worksheets, which use the same proportional reasoning, and area and perimeter worksheets, which show how resizing a figure affects its measurements. Together, these worksheets build a fuller picture of how shapes relate to one another in geometry class.