Free Printable WorksheetMathGeometryMath CurriculumG-GPE.A.1

GEO.142 Derive and use the equation of a circle Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.142 Derive and use the equation of a circle. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.142 Derive and use the equation of a circle - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select the correct equation of a circle from a center and radius (or graph) and determine whether a point lies on the circle. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.A.1; FL MA.912.GR.7.2-7.3; VA G.PC.4; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.142 Derive and use the equation of a circle skill assessments:

Problem 1Difficulty: Mastery
A circle has center (-5, -2) and passes through (1, 6). Which statement about the circle and point (3, 4) is correct?
AThe equation is (x - 5)2 + (y - 2)2 = 100, and (3, 4) is on the circle
BThe equation is (x + 5)2 + (y + 2)2 = 10, and (3, 4) is not on the circle
CThe equation is (x + 5)2 + (y + 2)2 = 100, and (3, 4) is not on the circle
DThe equation is (x + 5)2 + (y + 2)2 = 100, and (3, 4) is on the circle
Solution & Explanation:The squared radius from (-5, -2) to (1, 6) is 62 + 82 = 100. For (3, 4), the squared distance from the center is 82 + 62 = 100, so the point is on the circle.
Problem 2Difficulty: Mastery
The points (-1, 4), (3, 8), (7, 4), and (3, 0) are on a circle. Which equation represents the circle?
A(x + 3)2 + (y + 4)2 = 16
B(x - 3)2 + (y - 4)2 = 4
C(x - 3)2 + (y - 4)2 = 16
D(x - 4)2 + (y - 3)2 = 16
Solution & Explanation:The listed points are 4 units left, up, right, and down from (3, 4), so the center is (3, 4) and the radius is 4. Thus r2 = 16.
Problem 3Difficulty: Mastery
Point R(a, b) lies on the circle (x + 6)2 + (y - 2)2 = 65. Which expression must equal 65?
A(a - 6)2 + (b + 2)2
B(a + 6)2 + (b - 2)2
Ca2 + b2
D(a + 2)2 + (b - 6)2
Solution & Explanation:A point lies on a circle when its coordinates make the equation true. Replacing x with a and y with b gives (a + 6)2 + (b - 2)2 = 65.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-GPE.A.1 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select the correct equation of a circle from a center and radius (or graph) and determine whether a point lies on the circle. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.A.1; FL MA.912.GR.7.2-7.3; VA G.PC.4; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).

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