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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students predict and construct the image of a line under a dilation. They use the dilation center to decide whether the image coincides with the original line or runs parallel to it.
What Mastery Looks Like
- Given a center, scale factor, and line, students can construct the image using two points. They identify whether the image is the same line or a parallel line and justify their answer.
Common Misconceptions
- Students may think every line moves or changes slope during a dilation. They may also think a line through the center stays fixed point by point, rather than remaining the same line while its points move.
How to Assess It
- On a coordinate grid, dilate the lines y = x + 3 and y = 2x from the origin by a factor of 2. Graph both images and explain why each result differs.
Lesson moves
Ways to Teach It
Use patty paper to dilate two points on each line, connect the images, and compare the original and image lines.
Ask students to explain why a line can remain the same even though most points on it change position.
Sort diagram cards into two groups, same line or parallel line, then check each choice by tracing two image points.
Enlarge a street map from a marked center and identify which straight roads stay on the same path and which shift parallel.
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Printable HSG-SRT.A.1a Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSG-SRT.A.1a, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
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Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.G.A.3
Coordinate work with dilations helps students see how points on a line move and why image lines stay parallel or unchanged.
- CCSS.Math.Content.HSG-CO.A.1
Precise ideas of lines and parallel lines help students state and recognize how dilations move lines.
- CCSS.Math.Content.HSG-CO.A.2
Seeing transformations as point-to-point functions supports understanding how dilation maps every point on a line to its image line.
Keep exploring
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:
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