Cogito
Grade 8 Math · Chapter 2 · Lesson 3
Dilations on the Coordinate Plane
Multiply both coordinates by the scale factor.
10 problems · about 19 minutes · 8.G.A.3
What this lesson teaches
The child finds the coordinates of a dilated figure centred at the origin.
- A dilation from the origin multiplies both coordinates by the scale factor.
- Above 1 enlarges, between 0 and 1 shrinks.
- Angles are unchanged, which is why the result is similar rather than congruent.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Similar Figures: Similar figures. 4 matches 10. Another side is 6. Its match?
Answer 15
Why 15.
Review — Dilations: A side of 9 dilated by 3. New length?
Answer 27
Why 27.
Review — Sequences of Moves: Rotated 90° three times. Total turn in degrees?
Answer 270
Why 270°.
Warm Up
Straightforward practice. Get the method working first.
3 problems(4, −3) dilated by 5. What is the new y?
Answer -15
Why (20, −15).
(2, 7) dilated by 3. What is the new y?
Answer 21
Why 7 × 3.
(10, 6) dilated by ½. What is the new x?
Answer 5
Why Half of 10.
Build It Up
The same ideas with more to keep track of.
2 problemsDoes a dilation change the angles? 1 for yes, 0 for no.
Answer 0
Why Shape is preserved.
A factor of 1. How many times bigger is the figure?
Answer 1
Why Nothing changes.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Enlargement: (3, 5) dilated by 2 from the origin. What is the new x?
Answer 6
Why (6, 10).
The Reduction: (8, 4) dilated by ½ from the origin. What is the new y?
Answer 2
Why (4, 2).