In this Warm-up, students analyze the results of the transformation rule . They connect the geometric definition of a dilation to this coordinate rule that produces a dilation.

The goal of the discussion is to connect the geometric definition of a dilation to the coordinate rule . Here are some questions for discussion:

• “Why does it make sense that the ratios of the legs of the triangles were both ?” (This is because we multiplied each coordinate by 3, and the legs are just the vertical and horizontal distances to the points.)
• “Look at the definition of a dilation on your reference chart. How does it match what’s happening in the coordinate rule ?” (For scale factor , a dilation takes a point times farther away from the center of dilation. Here, the rule took the image of 3 times farther from the origin than the original.)

In this activity, students match graphs to rules in coordinate transformation notation. Then they analyze both the rules and images to decide which represent similarity transformations and which represent rigid transformations.

Students will use a variety of strategies to explain which figures are similar or congruent (counting, the Pythagorean Theorem, recognizing right angles, properties of isosceles triangles, and trigonometry). Monitor for students who use these different methods.

In this activity, students work backward to figure out a transformation rule. They are given the opportunity to come up with their own method of organizing their work. Monitor for students who have methods of clearly documenting information they are given as well as students who record their attempts at a rule. After students write a rule, they analyze the figures to decide if the transformation takes shapes to congruent shapes.

When students articulate their reasoning, they have an opportunity to attend to precision in the language they use to describe their thinking (MP6). They might first propose less formal or imprecise language, and after sharing with a partner, revise their explanation to be clearer and stronger.