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).
- Comprehend the terms scale factor and dilation.
- Critique and create scaled drawings of figures (using words and other representations).
- Let’s make a scale drawing.
- I can dilate a figure given a scale factor and center.
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 \(ABC\).
The factor by which every length in an original figure is increased or decreased when you make a scaled copy. For example, if you draw a copy of a figure in which every length is magnified by 2, then you have a scaled copy with a scale factor of 2.