What you’ll learn
Understand scale factors.
Key idea
One dimensionless multiplier must relate every corresponding length measured in the same units.
A dimensionless uniform scale must match every corresponding same-unit length; one correct side ratio is insufficient.
Worked example
Classify examples and non-examples for the concept 'Understand scale factors'.
Original rectangle 2cm by 5cm maps to 3cm by 17/2cm, corresponding sides in that order. Classify whether k=3/2 uniformly scales it.
- The original-to-image length ratio is 3/2=3/2.
- The other ratio is 17/2/5=17/10; they differ, so this is not a uniform scale drawing.
Answer: Non-example — the corresponding ratios differ; one equals 3/2 and the other 17/10.
Quick Check
Classify examples and non-examples for the concept 'Understand scale factors'.
Original rectangle 3cm by 2cm maps to 6cm by 4cm, corresponding sides in that order. Classify whether k=2 uniformly scales it.