Question

HELP! Select the correct answer.

Consider figures 1 through 4 on the coordinate plane. Which statement about these figures is true?

A. Figures 1 and 4 are congruent because figure 1 can be mapped onto figure 4 by a reflection and then a translation.
B. Figures 3 and 4 are not congruent because figure 3 can be mapped onto figure 4 by a vertical and horizontal translation.
C. Figures 2 and 3 are not congruent because figure 2 cannot be mapped onto figure 3 using a sequence of rigid transformations.
D. Figures 1 and 2 are congruent because figure 1 cannot be mapped onto figure 2 using a sequence of rigid transformations.

Answer 1

A. Figures 1 and 4 are congruent because figure 1 can be mapped onto figure 4 by a reflection and then a translation.

Explanation:

You want to know which statement about the congruence of the figures shown is true.

Congruence

Figures 1 and 4 have the same aspect ratio and general shape. They are congruent. Likewise for figures 2 and 3. However figures 1 and 2 have different aspect ratios (ratio of length to width), so cannot be congruent. Congruent figures can always be mapped to one another by rigid transformations.

Choices B, C, and D exhibit errors related to congruence or possible mappings, so are all false. The correct statement is ...

A. Figures 1 and 4 are congruent because figure 1 can be mapped onto figure 4 by a reflection and then a translation.

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