Cogito
Grade 8 Math · Chapter 2 · Lesson 1
Dilations
The move that does change size.
10 problems · about 18 minutes · 8.G.A.3
What this lesson teaches
The child describes a dilation and its effect on lengths and angles.
- A dilation multiplies every length by a scale factor.
- Angles are unchanged.
- It is not a rigid motion, because lengths change.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — Sequences of Moves: Rotated 90° three times. Total turn in degrees?
Answer 270
Why 270°.
Review — What a Transformation Does to Coordinates: (6, −2) translated 3 left. What is the new x?
Answer 3
Why (3, −2).
Warm Up
Straightforward practice. Get the method working first.
4 problemsA side of 9 dilated by 3. New length?
Answer 27
Why 27.
What does a dilation leave unchanged?
Answer The angles.
Why Angles survive; lengths do not.
A side of 5 dilated by 4. New length?
Answer 20
Why 5 × 4.
A side of 12 dilated by 1/2. New length?
Answer 6
Why Halved.
Build It Up
The same ideas with more to keep track of.
2 problemsAn angle of 75 dilated by 2. What is it now?
Answer 75
Why Unchanged.
Is a dilation a rigid motion?
Answer No. Lengths change.
Why Rigid means lengths survive.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Enlargement: A side of 7 is dilated by 3. How long is it now?
Answer 21
Why 21.
The Angle: An angle of 40 degrees is dilated by 5. What is it now?
Answer 40 degrees
Why Still 40 degrees.