Course
MATH C972 TASK 4: (Latest 2026/2027 Update) with Complete
Solutions
Curtis Allen
C972 task 4
A. Demonstrate, using an example, that the result of performing two
isometries— called isometry P and isometry Q—is not always
commutative (i.e., P○Q does not always equal Q○P). Show and explain
all steps.
Notes:
1: Initial Triangle; A = (2, 2), B = (5, 2), C = (5, 4).
2: Isometry P; rotate clockwise 90 degrees around the point (-4, 2).
3: Isometry Q; reflect across the x-axis.
, An example figure is established. Triangle ABC, consisting of point A (2,
2), B (5,
2), and C (5, 4). Isometries for P○Q and Q○P will be taken from this
figure (ABC).
Evaluation P○Q: The initial step is evaluating the isometry Q; (with the
triangle ABC), isometry Q is reflected across the X-axis. This created
A’B’C’ at points A’ (2, -2), B’ (5, -2), C’ (5, -4).
MATH C972 TASK 4: (Latest 2026/2027 Update) with Complete
Solutions
Curtis Allen
C972 task 4
A. Demonstrate, using an example, that the result of performing two
isometries— called isometry P and isometry Q—is not always
commutative (i.e., P○Q does not always equal Q○P). Show and explain
all steps.
Notes:
1: Initial Triangle; A = (2, 2), B = (5, 2), C = (5, 4).
2: Isometry P; rotate clockwise 90 degrees around the point (-4, 2).
3: Isometry Q; reflect across the x-axis.
, An example figure is established. Triangle ABC, consisting of point A (2,
2), B (5,
2), and C (5, 4). Isometries for P○Q and Q○P will be taken from this
figure (ABC).
Evaluation P○Q: The initial step is evaluating the isometry Q; (with the
triangle ABC), isometry Q is reflected across the X-axis. This created
A’B’C’ at points A’ (2, -2), B’ (5, -2), C’ (5, -4).
