In this activity, students recall the meaning of scaled drawings by studying an image and looking for a scaled copy and a distorted image. In the discussion, students should articulate that measurements in a scaled copy of a figure are the same multiple of measurements in the original figure.

The important concepts in this discussion are that in a scale drawing: 

• The ratio of the distance between two points in the original figure to the distance between two corresponding points in the scaled figure is constant.
• The corresponding angles are congruent.

Remind students of the term scale drawing from middle school. Ask students what they could measure to figure out which video game controller was a scale drawing of the original video game controller. (If the distance between the original controller’s buttons is twice the distance between the scaled controller’s buttons, then the height of the buttons on the original controller should also be twice the height of the buttons on the scaled controller.) If no student mentions angles, ask students if a protractor could also help them confirm which video game controller is the scale drawing. (The angles defined by points in the scaled figure should have the same measure as the angles defined by points in the original figure.) Students need not do any measuring.

Add the following definition to the class reference chart, and ask students to add it to their reference charts:

Scale factor is the factor by which every length in an original figure is multiplied when you make a scaled copy. (Definition)

This activity is the first time students are asked to dilate a figure in this course. Monitor for students with misconceptions, such as making the distance from to 120 units, rather than making the distance from to 120 units so that the distance from to is 80 units

In this activity, students dilate a figure with multiple points and multiple shapes. The goal is for them to practice dilation and begin to confirm some properties of dilation. Students will have additional opportunities to formalize properties of dilation in subsequent lessons. (A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. The dilation of a line segment is longer or shorter according to the same ratio given by the scale factor.)

Monitor for students who use these strategies, listed in order of precision:

• Use the two given lines to place and , and then estimate all of the other shapes and points.
• Measure distances within the figure, and try to replicate them, for example, calculating the radii of the two dilated circles and trying to place them without scaling and along rays through .
• Draw rays from through each point in the original figure, and place points in the image halfway between and the corresponding point.

When students articulate what they notice and wonder, they have an opportunity to attend to precision in the language they use to describe what they see (MP6). They might first propose less formal or imprecise language, and then restate their observation with more precise language in order to communicate more clearly.