MAFS.912.G-SRT.1.1

Verify experimentally the properties of dilations given by a center and a scale factor:
  1. 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.
  2. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
General Information
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
Assessed: Yes
Test Item Specifications

  • 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

Sample Test Items (1)
  • 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

This benchmark is part of these courses.
1200400: Foundational Skills in Mathematics 9-12 (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206300: Informal Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (course terminated))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
1206330: Analytic Geometry (Specifically in versions: 2014 - 2015 (course terminated))
7912060: Access Informal Geometry (Specifically in versions: 2014 - 2015 (course terminated))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 - 2022 (current), 2022 and beyond)
7912065: Access Geometry (Specifically in versions: 2015 - 2022 (current), 2022 and beyond)

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-SRT.1.AP.1b: Given a center and a scale factor, verify experimentally that when performing dilations of a line segment, the pre-image, the segment which becomes the image is longer or shorter based on the ratio given by the scale factor.

Related Resources

Vetted resources educators can use to teach the concepts and skills in this benchmark.

Assessments

Sample 1 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 4 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grades.

Type: Assessment

Sample 3 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Sample 2 - High School Geometry State Interim Assessment:

This is a State Interim Assessment for 9th-12th grade.

Type: Assessment

Formative Assessments

Dilation of a Line: Factor of Two:

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.

Type: Formative Assessment

Dilation of a Line: Factor of One Half:

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.

Type: Formative Assessment

Dilation of a Line Segment:

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

Type: Formative Assessment

Dilation of a Line: Center on the Line:

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.

Type: Formative Assessment

Lesson Plans

Coding Geometry Challenge #23 & 24:

This set of geometry challenges focuses on using transformations to show similarity and congruence of polygons and circles. Students problem solve and think as they learn to code using block coding software.  Student will need to use their knowledge of the attributes of polygons and mathematical principals of geometry to accomplish the given challenges. The challenges start out fairly simple and move to more complex situations in which students can explore at their own pace or work as a team. Computer Science standards are seamlessly intertwined with the math standards while providing “Step it up!” and “Jump it up!” opportunities to increase rigor.

Type: Lesson Plan

Discovering Dilations :

This resource is designed to give students the opportunity to discover the effects of dilations on geometric objects through the use of GeoGebra.

Type: Lesson Plan

Geometry Problems: Circles and Triangles:

This lesson unit is intended to help you assess how well students are able to use geometric properties to solve problems. In particular, the lesson will help you identify and help students who have the following difficulties:

  • Solving problems by determining the lengths of the sides in right triangles.
  • Finding the measurements of shapes by decomposing complex shapes into simpler ones.

The lesson unit will also help students to recognize that there may be different approaches to geometrical problems, and to understand the relative strengths and weaknesses of those approaches.

Type: Lesson Plan

Patterns in Fractals:

This lesson is designed to introduce students to the idea of finding patterns in the generation of several different types of fractals. This lesson provides links to discussions and activities related to patterns and fractals as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

Type: Lesson Plan

Problem-Solving Task

Dilating a Line:

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

Dilation and scale factor:

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

Type: Tutorial

MFAS Formative Assessments

Dilation of a Line Segment:

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

Dilation of a Line: Center on the Line:

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.

Dilation of a Line: Factor of One Half:

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.

Dilation of a Line: Factor of Two:

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

Vetted resources students can use to learn the concepts and skills in this benchmark.

Problem-Solving Task

Dilating a Line:

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

Dilation and scale factor:

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

Type: Tutorial

Parent Resources

Vetted resources caregivers can use to help students learn the concepts and skills in this benchmark.

Problem-Solving Task

Dilating a Line:

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

Type: Problem-Solving Task