Question

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

Explanation:

Step1: Recall the definition of similarity transformation

Similarity transformation includes translation, rotation, reflection and dilation. For two rectangles to be similar, the ratios of their corresponding side - lengths must be equal.

Step2: Analyze the side - length ratios

Let's assume the side - lengths of the smaller rectangle are \(a,b\) and the side - lengths of the larger rectangle are \(A,B\). For similarity, \(\frac{A}{a}=\frac{B}{b}\).
In the second graph (from the left), if we assume the smaller rectangle has length \(l_1\) and width \(w_1\), and the larger rectangle has length \(l_2\) and width \(w_2\), we can count the grid - units. Suppose the smaller rectangle has length \(l_1 = 3\) units and width \(w_1=2\) units, and the larger rectangle has length \(l_2 = 6\) units and width \(w_2 = 4\) units. Then \(\frac{l_2}{l_1}=\frac{6}{3}=2\) and \(\frac{w_2}{w_1}=\frac{4}{2}=2\).

Answer:

The second graph (from the left)