Similarity & Scale Factor Worksheet
Goal: Dilate a triangle by different scale factors, and discover how lengths, areas and volumes change with the scale factor.
What to do
- Open the transformation playground and press “Scale from origin”. The original triangle is A(−2, −1), B(2, −1), C(0, 2), with an area of 6 square units.
- For each scale factor in the table, type it into “Scale factor” and record A′, the new area and the area factor.
- Work out the length of side A′B′ from the coordinates of A′ and B′, and add it to the table.
Record your results
| Setting | A′ | A′B′ length | New area | Area factor |
|---|---|---|---|---|
| Scale factor 0.5 | ||||
| Scale factor 1 | ||||
| Scale factor 1.5 | ||||
| Scale factor 2 | ||||
| Scale factor 3 |
Questions
The original side AB is 4 units long. How does the length of A′B′ compare with the scale factor?
Look at the area factor column. How is it related to the scale factor?
Predict the new area for a scale factor of 2.5, then check it with the tool.
A map has a scale of 1 : 50,000. Two towns are 6 cm apart on the map. How far apart are they in real life? A park covers 2 cm² on the map: what is its real area?
A cube with 3 cm edges is scaled by a factor of 2. Find the new surface area and volume, and compare the growth with k² and k³.
Is a dilation with scale factor 1 a similarity? With scale factor 0.5, is the image similar to the original?
Free from Geometry Lab · geometrylab.net · 7.G.A.1: Solve problems involving scale drawings, including computing actual lengths and areas from a scale drawing. HSG-SRT.A.1: Verify experimentally the properties of dilations given by a center and a scale factor. 8.G.A.3: Describe the effect of dilations, translations, rotations and reflections on two-dimensional figures using coordinates.
Teaching with this? Find the answer key and more activities on the Geometry Lab for teachers page.