What you’ll learn
Define similarity using transformations.
Key idea
Rigid motion preserves a positive side length; only the dilation scales it.
Orientation reversal does not make a length negative; only dilation changes size.
Worked example
Enter the exact value or ordered values in the format requested below.
A triangle side length 6 is reflected and then dilated by positive factor 1/2. Find the corresponding final side length.
- Reflection preserves original side length 6.
- Dilation multiplies it by 1/2, giving 3; inverse ratio 3/6=1/2.
Answer: 3
Quick Check
Evaluate a worked attempt at define similarity using transformations, identify the first invalid step, and provide the correction.
A triangle side length 11 undergoes reflection then dilation k=1/2. Student Step 1 makes reflected length -11 due to orientation reversal; Step 2 scales it to -11/2. Find first invalid step and correct final length.