Cogito
Geometry · Chapter 2 · Lesson 3
Dilations and Scale Factor
The one transformation that changes size.
11 problems · about 22 minutes · G-SRT.A.1
What this lesson teaches
The student applies a dilation and predicts its effect on lengths and areas.
- A dilation multiplies both coordinates by the scale factor.
- Angles are unchanged, so the image is similar rather than congruent.
- Lengths scale by k, areas by k², and volumes by k³.
Warm Up
Straightforward practice. Get the method working first.
4 problemsArea 4, factor 3. New area?
Answer 36
Why 36.
(3, 7) dilated by 4. New y?
Answer 28
Why 7 × 4.
Area 6, factor 3. New area?
Answer 54
Why × 9.
Factor 5. By what does area scale?
Answer 25
Why k².
Build It Up
The same ideas with more to keep track of.
3 problemsDoes a dilation change angles? 1 for yes, 0 for no.
Answer 0
Why Shape is preserved.
(8, 6) dilated by ½. New x?
Answer 4
Why Half of 8.
A factor of 1. Is the figure unchanged? 1 for yes, 0 for no.
Answer 1
Why Nothing is scaled.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsVolume scales by which power of k? Give the power.
Answer 3
Why Three dimensions.
Sort each quantity by how it scales under a dilation of factor k.
Answer By k: Side length, Perimeter · By k²: Area · Unchanged: Angle measure
Why Perimeter is a length, however many sides it adds up.
The Point: (4, 5) dilated by 3 from the origin. New x?
Answer 12
Why 12.
The Area: Area 5, dilated by factor 2. New area?
Answer 20
Why 20.