WGU C992 Task 4 Passed (2026) – Counterexamples | College Geometry

C992
College Geometry
TASK 4 – Passed
Counterexamples
Western Governors University

, College Geometry – C992

Task 4 – Counterexamples

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.

Isometries, also called rigid transformations, are transformations that do not change the size or shape
of the preimage(Bass 2023). Examples of isometries include translations, rotations, and reflections.




Above is the original triangle created. Starting with the points A (4,4), B (4,10), and C (12,4), triangle
ABC is formed. The side lengths of triangle ABC are a = 10, b = 8 and c = 6. The angle measures of
triangle ABC are y = 90°, α = 53.13° and β = 36.87°.




Above shows the application of Isometry P (a reflection across the x axis) to triangle ABC. This
reflection transforms the points (x, y)  (x, -y). The reflection does not affect the side lengths. The
reflection does not affect the angle measures.

Point A (4, 4)  A’ (4, -4)

Point B (4, 10)  B’ (4, -10)




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