Question

grid transformations.

1. the transformations given are performed on pentagon abcde to create pentagon abcde.

• (x, y) → (x - 5, y - 6)
• counterclockwise rotation of 37° about the origin

complete the sentence to explain whether or not the pentagons are congruent.
pentagons abcde and abcde
are are not
congruent because
a. each
b. neither
c. only the first
d. only the second
transformation preserves side lengths and angle measures.

Explanation:

Step1: Analyze the first transformation

The first transformation is a translation: \((x, y) \to (x - 5, y - 6)\). Translations are rigid transformations, which means they preserve the shape and size of the figure, so side lengths and angle measures remain the same.

Step2: Analyze the second transformation

The second transformation is a counterclockwise rotation of \(37^\circ\) about the origin. Rotations are also rigid transformations, meaning they preserve the shape and size of the figure, so side lengths and angle measures remain the same.

Step3: Determine congruence

Since both transformations (translation and rotation) are rigid transformations, they preserve the side lengths and angle measures of the pentagon. Therefore, the original pentagon \(ABCDE\) and the transformed pentagon \(A'B'C'D'E'\) should be congruent because both transformations preserve the necessary properties for congruence.

Answer:

are; a. each