- 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 in the ratio given by the scale factor.

**Subject Area:**Mathematics

**Grade:**912

**Domain-Subdomain:**Geometry: Similarity, Right Triangles, & Trigonometry

**Cluster:**Level 2: Basic Application of Skills & Concepts

**Cluster:**Understand similarity in terms of similarity transformations. (Geometry - Major Cluster) -

Clusters should not be sorted from Major to Supporting and then taught in that order. To do so would strip the coherence of the mathematical ideas and miss the opportunity to enhance the major work of the grade with the supporting clusters.

**Date Adopted or Revised:**02/14

**Date of Last Rating:**02/14

**Status:**State Board Approved - Archived

**Assessed:**Yes

**Assessment Limits :**

Items may use line segments of a geometric figure.The center of dilation and scale factor must be given.

**Calculator :**Neutral

**Clarification :**

When dilating a line that does not pass through the center of dilation,

students will verify that the dilated line is parallel.When dilating a line that passes through the center of dilation,

students will verify that the line is unchanged.When dilating a line segment, students will verify that the dilated line

segment is longer or shorter with respect to the scale factor.**Stimulus Attributes :**

Items may give the student a figure or its dilation, center, and scale

and ask the student to verify the properties of dilation.Items may be set in a real-world or mathematical context.

**Response Attributes :**None

**Test Item #:**Sample Item 1**Question:**Quadrilateral MATH is shown.

Quadrilateral MATH is dilated by a scale factor of 2.5 centered at (1,1) to create quadrilateral M'A'T'H'. Select all the statements that are true about the dilation.

**Difficulty:**N/A**Type:**MS: Multiselect

## Related Courses

## Related Access Points

## Related Resources

## Formative Assessments

## Lesson Plans

## Problem-Solving Task

## Tutorial

## MFAS Formative Assessments

Students are asked to dilate a line segment and describe the relationship between the original segment and its image.

Students are asked to graph the image of two points on a line after a dilation using a center on the line and to generalize about dilations of lines when the line contains the center.

Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center.

Students are asked to graph the image of three points on a line after a dilation using a center not on the line and to generalize about dilations of lines when the line does not contain the center.

## Student Resources

## Problem-Solving Task

This task asks students to make deductions about a line after it has been dilated by a factor of 2.

Type: Problem-Solving Task

## Tutorial

In this tutorial, students will use a scale factor to dilate one line onto another.

Type: Tutorial

## Parent Resources

## Problem-Solving Task

This task asks students to make deductions about a line after it has been dilated by a factor of 2.

Type: Problem-Solving Task