Question

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

Explanation:

Step1: Recall the definition of similar rectangles

Similar rectangles have corresponding sides in proportion.

Step2: Analyze each graph

• In the first graph, the side - length ratios are not consistent.
• In the second graph, assume the smaller rectangle has length \(l_1\) and width \(w_1\), and the larger rectangle has length \(l_2\) and width \(w_2\). If we count the grid units, we can find that \(\frac{l_2}{l_1}=\frac{w_2}{w_1}\) (by counting the number of horizontal and vertical units for the sides of the rectangles). A similarity transformation (a dilation) can be used.
• In the third graph, the side - length ratios are not consistent.
• In the fourth graph, the side - length ratios are not consistent.

Answer:

The second graph.