Free Printable WorksheetMathGeometryMath CurriculumG-CO.C.10

GEO.68 Loci and geometric constructions as sets of points Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.68 Loci and geometric constructions as sets of points. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.68 Loci and geometric constructions as sets of points - Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.C.10. Skill statement in this prompt cell: Select the construction or diagram that represents the correct locus for a stated condition (equidistant from points, lines, or rays). Associated standards listed with this skill in the curriculum source: CCSS G-CO.C.10; FL MA.912.GR.1.3; MA G-CO.C.10; NY GEO G.G-CO.C.10; TEKS §111.41(c); CCSS G-CO.D.12-13; FL MA.912.GR.5.1-5.3; MA G-CO.D.12-13. 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.68 Loci and geometric constructions as sets of points skill assessments:

Problem 1Difficulty: Mastery
Which option correctly evaluates this statement: The locus of points equidistant from a point and a line not containing that point is a parabola with the point as focus and the line as directrix?
AFalse, because that condition defines a circle centered at the point
BFalse, because the locus must be a perpendicular bisector of a segment
CTrue, but only when the point lies on the line
DTrue, because that is the focus-directrix definition of a parabola
Solution & Explanation:The statement is true. A parabola is defined as the set of points equidistant from a fixed point, called the focus, and a fixed line, called the directrix.
Problem 2Difficulty: Mastery
A point P lies on an angle bisector of two intersecting lines. Which distance statement correctly explains why P is on the equidistant locus?
AThe distances from P to any two points on the lines are equal
BThe distance from P to the intersection is zero
CThe perpendicular distances from P to the two lines are equal
DThe angle bisector is parallel to both lines
Solution & Explanation:The angle-bisector locus is based on perpendicular distance to each line. Being on the angle bisector guarantees those perpendicular distances are equal.
Problem 3Difficulty: Mastery
A student compares two diagrams for points equidistant from A and B: Diagram 1 shows line AB, and Diagram 2 shows the perpendicular bisector of AB. Which diagram is correct and why?
ADiagram 1, because points on AB are always the same distance from A and B
BDiagram 2, because every point on the perpendicular bisector is the same distance from A and B
CBoth diagrams, because any line touching AB is a locus
DNeither diagram, because only circles can represent loci
Solution & Explanation:Line AB contains only one point equidistant from A and B: the midpoint. The complete locus is Diagram 2, the perpendicular bisector of AB.

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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-CO.C.10 (Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.C.10. Skill statement in this prompt cell: Select the construction or diagram that represents the correct locus for a stated condition (equidistant from points, lines, or rays). Associated standards listed with this skill in the curriculum source: CCSS G-CO.C.10; FL MA.912.GR.1.3; MA G-CO.C.10; NY GEO G.G-CO.C.10; TEKS §111.41(c); CCSS G-CO.D.12-13; FL MA.912.GR.5.1-5.3; MA G-CO.D.12-13. Use this prompt-provided wording as the supporting standard description for this workflow.).

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