Question

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

Explanation:

Step1: Recall the concept 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 each graph

• In the first graph, the side - length ratios of the two rectangles are not equal.
• In the second graph, the side - length ratios of the two rectangles are not equal.
• In the third graph, assume the side lengths of the smaller rectangle are \(l_1\) and \(w_1\), and the side lengths of the larger rectangle are \(l_2\) and \(w_2\). By counting the grid units, we can find that \(\frac{l_2}{l_1}=\frac{w_2}{w_1}\) (for example, if the smaller rectangle has length \(3\) units and width \(2\) units, and the larger rectangle has length \(6\) units and width \(4\) units, \(\frac{6}{3}=\frac{4}{2} = 2\)).
• In the fourth graph, the side - length ratios of the two rectangles are not equal.

Answer:

The third graph.