Free Printable WorksheetMathGeometryMath CurriculumG-GPE.A.1

GEO.150 Determine whether a point lies on 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.150 Determine whether a point lies on a circle. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.150 Determine whether a point lies on a circle - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.A.1. Skill statement in this prompt cell: Select whether a given point lies on a circle based on its equation and the point's coordinates. 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.150 Determine whether a point lies on a circle skill assessments:

Problem 1Difficulty: Mastery
For x2 + y2 - 4x + 10y + 20 = 0, determine whether P(4, -7) lies on the circle.
AYes, because the standard form is (x - 2)2 + (y + 5)2 = 9 and P gives 8.
BNo, because the standard form is (x - 2)2 + (y + 5)2 = 9 and P gives 8.
CYes, because substituting gives -1.
DNo, because the circle's center is P.
Solution & Explanation:Completing the square gives (x - 2)2 + (y + 5)2 = 9. For P(4, -7), the value is 22 + (-2)2 = 8, so P does not lie on the circle.
Problem 2Difficulty: Mastery
For (x - 2)2 + (y - 2)2 = 13, the labeled points are A(5, 4), B(-1, 0), C(6, 3), and D(2, -2). Which points lie on the circle?
AA and B only
BA and C only
CB and D only
DC and D only
Solution & Explanation:A gives (3)2 + (2)2 = 13, and B gives (-3)2 + (-2)2 = 13. C gives 17 and D gives 16, so only A and B lie on the circle.
Problem 3Difficulty: Mastery
A student says P(-3, 4) is not on x2 + y2 = 25 because -3 + 4 = 1. Which critique is correct?
AThe student is correct because coordinates should be added.
BThe student is incorrect because the test is (-3)2 + 42 = 25, so P lies on the circle.
CThe student is correct because negative x-values cannot be on this circle.
DThe student is incorrect because every point in quadrant II lies on the circle.
Solution & Explanation:For x2 + y2 = 25, square the coordinates before adding. Since 9 + 16 = 25, P lies on the circle.

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Frequently Asked Questions

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QIs this GEO.150 Determine whether a point lies on a circle worksheet free for teachers and homeschoolers?

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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 whether a given point lies on a circle based on its equation and the point's coordinates. 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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