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MAFS.912.G-GPE.1.1

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

General Information

Subject Area: Mathematics
Grade: 912
Domain-Subdomain: Geometry: Expressing Geometric Properties with Equations
Cluster: Level 2: Basic Application of Skills & Concepts
Cluster: Translate between the geometric description and the equation for a conic section. (Geometry - Additional Cluster) (Algebra 2 - Additional 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 :
    In items where the student has to complete the square to find the
    center and radius of the circle, coefficients of quadratic terms should
    equal 1 and all other terms should have integral coefficients.
  • Calculator :

    Neutral

  • Clarification :
    Students will use the Pythagorean theorem, the coordinates of a
    circle’s center, and the circle’s radius to derive the equation of a
    circle.

    Students will determine the center and radius of a circle given its
    equation in general form. 

  • Stimulus Attributes :
    Items may be set in a real-world or mathematical context.
  • Response Attributes :
    Items may require the student to draw a circle that matches an
    equation in general form.

Sample Test Items (1)

  • Test Item #: Sample Item 1
  • Question:

    Johnny wants to find the equation of a circle with center (3,-4) and a radius of 7. He uses the argument shown.

    There are three highlights in the argument to show missing words or phrases. For each highlight, click on the word of phrase that correctly fills the blank.

  • Difficulty: N/A
  • Type: ETC: Editing Task Choice

Related Courses

This benchmark is part of these courses.
1200400: Intensive Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1202340: Pre-Calculus (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1207310: Liberal Arts Mathematics (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206310: Geometry (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206320: Geometry Honors (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1298310: Advanced Topics in Mathematics (formerly 129830A) (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
1206315: Geometry for Credit Recovery (Specifically in versions: 2014 - 2015, 2015 and beyond (current))
7912065: Access Geometry (Specifically in versions: 2015 and beyond (current))

Related Access Points

Alternate version of this benchmark for students with significant cognitive disabilities.
MAFS.912.G-GPE.1.AP.1b: Given the equation, find the center and the radius of a circle.

Related Resources

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

Assessments

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

Complete the Square for Center-Radius 2:

Students are asked to find the center and radius of a circle given its equation in general form.

Type: Formative Assessment

Derive the Circle – General Points:

Students are given the coordinates of the center, (h, k), and the radius, r, of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Type: Formative Assessment

Derive the Circle – Specific Points:

Students are given the coordinates of the center and the radius of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Type: Formative Assessment

Complete the Square for Center-Radius:

Students are asked to find the center and radius of a circle given its equation in general form.

Type: Formative Assessment

Lesson Plans

Circle Reasoning:

Students use the Pythagorean Theorem (Distance Formula) to derive the Standard Equation of a Circle; then move between descriptions and equations of a circle.

Type: Lesson Plan

Equations of Circles 1:

This lesson unit is intended to help you assess how well students are able to use the Pythagorean theorem to derive the equation of a circle and translate between the geometric features of circles and their equations.

Type: Lesson Plan

Equations of Circles 2:

This lesson unit is intended to help you assess how well students are able to translate between the equations of circles and their geometric features and sketch a circle from its equation.

Type: Lesson Plan

Run Fido, Run!:

Students are guided through a lesson finding the equation of a circle on a Cartesian Coordinate plane.

Then they look for the best place to tether their dog in the backyard in order to continue to explore circles and their equations.

Type: Lesson Plan

Original Student Tutorials

Where IS that Cell Tower?:

Find the location and coverage area of cell towers by completing the square to determine the center and radius of a circle given its equation in this interactive tutorial. 

Type: Original Student Tutorial

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions on this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Slopes and Circles:

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle

Type: Problem-Solving Task

MFAS Formative Assessments

Complete the Square for Center-Radius:

Students are asked to find the center and radius of a circle given its equation in general form.

Complete the Square for Center-Radius 2:

Students are asked to find the center and radius of a circle given its equation in general form.

Derive the Circle – General Points:

Students are given the coordinates of the center, (h, k), and the radius, r, of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Derive the Circle – Specific Points:

Students are given the coordinates of the center and the radius of a circle and are asked to derive the equation of the circle using the Pythagorean Theorem.

Original Student Tutorials Mathematics - Grades 9-12

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions on this interactive tutorial.

Where IS that Cell Tower?:

Find the location and coverage area of cell towers by completing the square to determine the center and radius of a circle given its equation in this interactive tutorial. 

Student Resources

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

Original Student Tutorials

Where IS that Cell Tower?:

Find the location and coverage area of cell towers by completing the square to determine the center and radius of a circle given its equation in this interactive tutorial. 

Type: Original Student Tutorial

Circle Up!:

Learn how to write the equation of a circle using Pythagorean Theorem given its center and radius using step-by-step instructions on this interactive tutorial.

Type: Original Student Tutorial

Problem-Solving Task

Slopes and Circles:

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle

Type: Problem-Solving Task

Parent Resources

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

Problem-Solving Task

Slopes and Circles:

The purpose of this task is to lead students through an algebraic approach to a well-known result from classical geometry, namely, that a point X is on the circle of diameter AB whenever ?AXB is a right angle

Type: Problem-Solving Task