Question

question 14 of 25

which of these terms does not describe polygon \\(abcd\\)?

a. image
b. preimage
c. rotation
d. transformation

Explanation:

Identify the roles of the polygons

The original polygon is \(ABCD\), which is the preimage. The transformed polygon is \(A'B'C'D'\), which is the image resulting from a geometric transformation.

Analyze the transformation type

Comparing the coordinates of \(ABCD\) and \(A'B'C'D'\):

• \(A(2, 5)

ightarrow A'(-5, 4)\)

• \(B(2, 7)

ightarrow B'(-5, 7)\)

• \(C(6, 7)

ightarrow C'(-7, 7)\)

• \(D(6, 5)

ightarrow D'(-7, 4)\)
The orientation and shape have changed via a reflection and/or translation, but it is not a rotation. More importantly, \(A'B'C'D'\) is specifically the "image" and the result of a "transformation", whereas \(ABCD\) is the "preimage".

Evaluate the given options

• A. "image": Describes \(A'B'C'D'\) correctly.
• B. "preimage": Describes \(ABCD\), not \(A'B'C'D'\). Thus, "preimage" does not describe \(A'B'C'D'\).
• C. "rotation": While the transformation is a reflection, "preimage" is fundamentally incorrect as it describes the starting figure.
• D. "transformation": Describes the process that created \(A'B'C'D'\).

Therefore, "preimage" is the term that definitely does not describe the resulting polygon \(A'B'C'D'\).

Answer:

• A. image
• B. preimage (Correct answer)
• C. rotation
• D. transformation