Question

which graph has figures that can undergo a similarity transformation to justify that they are similar?

Explanation:

Step1: Recall Similarity Transformation

Similarity transformations (scaling, rotation, reflection, translation) preserve shape (angles) and have proportional sides. For rectangles, check if length/width ratios are equal.

Step2: Analyze Each Graph

• First Graph: Small square (1x1), large rectangle (e.g., 4x3). Ratios 1/1 vs 4/3: not equal.
• Second Graph: Let’s assume grid units. Suppose inner rectangle: length \( l_1 \), width \( w_1 \); outer: \( l_2 \), \( w_2 \). Check \( \frac{l_2}{l_1} = \frac{w_2}{w_1} \). If inner is, say, 4x2, outer 6x3: \( \frac{6}{4} = \frac{3}{2} = 1.5 \). Proportional.
• Third Graph: Sides may not scale proportionally (e.g., inner length 5, outer 6; inner width 3, outer 4: \( \frac{6}{5}

eq \frac{4}{3} \)).

• Fourth Graph: Shapes (square and rectangle) have different aspect ratios (1 vs non - 1), so not similar.

Answer:

The Second Graph (the middle - left among the four, or the second one in the sequence)