Unit 2, Lesson 9
Dilations
Accelerated 7
Preparation
Lesson Narrative
This lesson formally defines the term dilation as a transformation in which each point on a figure moves along a line and changes its distance from a fixed point, called the center of dilation. The scale factor determines how far each point moves.
Students are introduced to the circular grid as an effective tool for performing a dilation. By using the structure of the grid, they find that each grid circle maps to a grid circle, line segments map to line segments, and the image of a polygon is a scaled copy of the polygon (MP7). Then students apply dilations to points with no grid to make perspective drawings. In order to perform a dilation with no grid, three pieces of information are still needed: a center of dilation, a scale factor, and a point to be dilated.
- Create a dilation of a figure given a scale factor and center of dilation.
- Explain (orally) how a dilation affects the size, side lengths and angles of polygons.
- Explain (orally) the effect of the scale factor on the size of the image of a polygon and its distance from the center of dilation.
Let's dilate figures.
Required Preparation
Provide access to straightedges. For the digital version of the activity, acquire devices that can run the applet.
Provide access to geometry toolkits.
Provide access to geometry toolkits.
A dilation is a transformation that can reduce or enlarge a figure. Each point on the figure moves along a line closer to or farther from a fixed point. That fixed point is the center of the dilation. All of the original distances are multiplied by the same scale factor.
Triangle is a dilation of triangle . The center of dilation is . The scale factor is 3.
Every point of triangle is 3 times as far from as every corresponding point of triangle .