Question

9.
melanie and james were discussing the figures shown in the graph
below. melanie says that the two figures are congruent. which of these is
the best way for melanie to explain why she considers the figures
congruent?

(graph with two figures labeled w and y, coordinate axes with -10, -5, 0, 5, etc. and a blue crown - like figure w near -5 to 0 on the x - axis and 0 to 5 on the y - axis, and figure y near 0 to 5 on the x - axis and below 0 on the y - axis)

Explanation:

(Note: Since the graph's full details (like the second figure's exact position/shape transformation) aren't fully clear, but congruent figures can be explained via transformations. Here's a general approach.)

Step1: Recall Congruence Definition

Congruent figures have same shape/size, related by rigid transformations (translation, rotation, reflection).

Step2: Analyze Transformations

Check if figure W can be transformed (e.g., rotate, translate, reflect) to match figure Y. If after rotation (e.g., 90°/180°), translation, and reflection, vertices align, they're congruent.

Step3: Explain the Best Way

Melanie should show one figure is image of the other under rigid transformations (e.g., "One figure can be rotated, translated, or reflected to exactly match the other, so they have same shape/size (congruent).")

Answer:

Melanie should explain that the two figures are congruent because one can be mapped onto the other using rigid transformations (translation, rotation, reflection), meaning they have the same shape and size. (If options were given, pick the one describing rigid transformations matching the figures' relationship.)