NY Next Generation Math GEO-G.SRT.1.a
The Standard
Verify experimentally that 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.
New York State Next Generation Mathematics Learning Standards
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students experimentally verify how dilation affects lines. A line away from the center maps to a parallel line, while a line through the center remains on itself.
What Mastery Looks Like
- The student dilates multiple points on each type of line and identifies the image line accurately. Measurements or slope evidence supports the conclusion.
Common Misconceptions
- Students may say the through-center line stays pointwise fixed or that every image line is parallel and distinct. They may omit the dilation center when explaining the result.
How to Assess It
- Give one line through a dilation center and one line away from it. Ask students to map two points on each and state the resulting line relationship.
Lesson moves
Ways to Teach It
Dilate point pairs on two strings, one crossing the center and one offset, then compare image lines.
Ask which points on a through-center line move even though the image line is unchanged.
Play line-image match with dilation centers, original lines, and possible image lines.
Use perspective projection rays to explain why parallel cross-sections appear at different sizes.
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Printable GEO-G.SRT.1.a Worksheet
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Related Standards
- NY-8.G.1.c
Verify experimentally parallel lines are mapped to parallel lines.
- NY-8.G.1.a
Verify experimentally lines are mapped to lines, and line segments to line segments of the same length.
- GEO-G.SRT.1
Verify experimentally the properties of dilations given by a center and a scale factor.
- GEO-G.SRT.1.b
Verify experimentally that the dilation of a line segment is longer or shorter in the ratio given by the scale factor.
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