Cogito
Integrated Math 2 · Chapter 4 · Lesson 1
Dilations and Scale Factor
Changing size without changing shape.
12 problems · about 21 minutes · G-SRT.A.1, G-SRT.A.2
What this lesson teaches
The student performs dilations and describes their effect on lengths, angles and area.
- A dilation multiplies every distance from a centre by the scale factor.
- Angles are unchanged, so the shape is preserved.
- Area scales by k² and volume by k³.
Warm Up
Straightforward practice. Get the method working first.
5 problemsAn area of 10 is dilated by a factor of 3. What is the new area?
Answer 90
Why 90.
Why does area scale by the square of the factor?
Answer Area is a product of two lengths, and both are multiplied.
Why Two scaled lengths multiply to give k².
Length 8 dilated by factor 2. New length?
Answer 16
Why 8 × 2.
Area 20 dilated by factor 2. New area?
Answer 80
Why 20 × 4.
Volume 5 dilated by factor 2. New volume?
Answer 40
Why 5 × 8.
Build It Up
The same ideas with more to keep track of.
3 problemsAn angle of 50° dilated by factor 3. What is the new angle, in degrees?
Answer 50
Why Angles do not change.
Length 12 dilated by factor 0.5. New length?
Answer 6
Why Half.
Area 36 dilated by factor 0.5. New area?
Answer 9
Why 36 × 0.25.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
4 problemsSort each quantity by whether a dilation changes it.
Answer Changes: Side lengths, Area · Stays the same: Angle measures, The overall shape
Why Shape is preserved precisely because angles are.
Area 7 dilated by factor 4. New area?
Answer 112
Why 7 × 16.
The Enlargement: A length of 5 is dilated by a factor of 3. What is the new length?
Answer 15
Why 15.
The Area: An area of 12 is dilated by a factor of 3. What is the new area?
Answer 108
Why 108.