What you’ll learn
Understand dilation scale factors.
Key idea
A positive factor multiplies all center-to-point distances by the same ratio; it is not a fixed added displacement.
One positive multiplier must work for every point; a single additive coincidence is not a dilation rule.
Worked example
Classify examples and non-examples for the concept 'Understand dilation scale factors'.
Center O=(0,0); proposed P=(2,5) to (4/3,10/3) and Q=(-5,2) to (-10/3,7/3). Is this one dilation? Give factor evidence or a failed constraint.
- First image is 2/3 times P, fixing the candidate scale.
- Test both Q coordinates: required (-10/3,4/3); proposed (-10/3,7/3) fails the second coordinate.
Answer: No — P fixes k=2/3, but Q image second coordinate should be 4/3, not 7/3.
Quick Check
Classify examples and non-examples for the concept 'Understand dilation scale factors'.
Center O=(0,0); proposed P=(3,5) to (9/2,15/2) and Q=(-5,3) to (-15/2,9/2). Is this one dilation? Give factor evidence or a failed constraint.