What you’ll learn
Define congruence through rigid motion.
Key idea
An axis-aligned segment length is the absolute coordinate difference; equate original and image lengths.
Rigid motions preserve nonnegative distance; coordinate or orientation sign is not a length sign.
Worked example
Enter the exact value or ordered values in the format requested below.
Segment A=(-3, -2), B=(-3, 0). Translation then x-axis reflection yields images [(-1, 3), (-1, 1)] under (u,v) to (u+2,-v+1). Find the image segment length.
- Original vertical segment A=(-3, -2), B=(-3, 0) has length 2.
- The rigid function (u,v) maps to (u+2,-v+1); images [(-1, 3), (-1, 1)] also differ by distance 2. The forward endpoint coordinate is 0.
Answer: 2
Quick Check
Evaluate a worked attempt at define congruence through rigid motion, identify the first invalid step, and provide the correction.
A=(-3, -1), B=(5, -1), rigid images [(-1, 2), (7, 2)]. Student: Step 1, original length is 8. Step 2, reflection reverses orientation so the image length is -8. Identify first invalid step and correct image length.