# Lesson 1

Scale Drawings

### Lesson Narrative

In middle school, students studied scale drawings and dilations. In this lesson students review the definition of scale factor by comparing an example and a non-example of a scaled image. We define scale factor as the factor by which every length in an original figure is increased or decreased when making a scaled copy.

In the subsequent activities students practice dilating points and figures. We define dilation as follows: A dilation with center $$P$$ and positive scale factor $$k$$ takes a point $$A$$ along the ray $$PA$$ to another point whose distance is $$k$$ times farther away from $$P$$ than $$A$$ is. In this lesson students begin to identify the properties of dilations (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.) but they do not formalize them until a subsequent lesson.

When students are drawing a dilation they must both measure precisely and pay attention to which of the labelled points is being used as the center (MP6).

### Learning Goals

Teacher Facing

• Comprehend the terms scale factor and dilation.
• Critique and create scaled drawings of figures (using words and other representations).

### Student Facing

• Let’s make a scale drawing.

### Student Facing

• I can dilate a figure given a scale factor and center.

Building On

Building Towards

### Glossary Entries

• dilation

A dilation with center $$P$$ and positive scale factor $$k$$ takes a point $$A$$ along the ray $$PA$$ to another point whose distance is $$k$$ times farther away from $$P$$ than $$A$$ is.

Triangle $$A'B'C'$$ is the result of applying a dilation with center $$P$$ and scale factor 3 to triangle $$ABC$$.