CCSS.Math.Content.HSG-SRT.A.1a
The standard
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.
Common Core State Standards for Mathematics · Understand similarity in terms of similarity transformations
What this standard means
Students need to understand what happens to lines under a dilation. If the center of dilation is on the line, the line stays in the same place. If the center is not on the line, the image of the line moves but stays parallel to the original line.
Mastery means students can predict the image before graphing, explain why the two lines are parallel, and identify the special case when the line is unchanged. Students often mix up dilation with translation, or think every point moves the same distance. They also get stuck when the center is not at the origin.
Ways to teach it
- Have students graph a line and a dilation center, dilate two points on the line with patty paper, then draw the image line.
- Prompt students to explain why a line through the dilation center does not become a new parallel line.
- Give three graphed lines and one dilation center, then ask students to label each image as parallel or unchanged.
- Show how enlarging a photo from one corner keeps edges through that corner fixed while opposite edges shift to parallel positions.
Plan a lesson for CCSS.Math.Content.HSG-SRT.A.1a
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Related standards
- CCSS.Math.Content.HSG-SRT.A.1b
The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
- CCSS.Math.Content.8.G.A.1c
Parallel lines are taken to parallel lines.
- CCSS.Math.Content.8.G.A.1a
Lines are taken to lines, and line segments to line segments of the same length.
- CCSS.Math.Content.HSG-SRT.A.1
Verify experimentally the properties of dilations given by a center and a scale factor: