What you’ll learn
Construct transformation sequences.
Key idea
Write an intermediate point before applying the second operation.
Correct individual operations in wrong order give a different transformation; compute the intermediate point.
Worked example
Enter the exact value or ordered values in the format requested below.
Point P=(-2,-2). Construct its final image under the required sequence: rotate 180 degrees about the origin, then translate by (-1,2). Enter the final ordered pair.
- From (-2,-2), first operation gives (2,2).
- Second operation gives (1,4); reversed order gives (3,0) and alternative gives (2,2). These endpoints differ.
Answer: (1,4)
Quick Check
Choose which candidate representation satisfies the requirements of 'Construct transformation sequences' and justify the choice.
P=(-2,-1), target (1,-1). Candidate A: rotate 180 degrees about the origin, then translate by (-1,-2). Candidate B: translate by (-1,-2), then rotate 180 degrees about the origin. Candidate C: rotate 180 degrees about the origin without translating. Select the sequence reaching target and justify via intermediate point.