Free Printable WorksheetMathGeometryMath CurriculumG-GPE.B.5

GEO.148 Determine collinearity and parallelism from coordinates Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.148 Determine collinearity and parallelism from coordinates. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.148 Determine collinearity and parallelism from coordinates - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.5. Skill statement in this prompt cell: Select whether points are collinear or whether lines are parallel based on computed slopes or coordinate differences. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.B.5; FL MA.912.GR.3.3; MA G-GPE.B.5; TEKS §111.41(c); CCSS G-GPE.B.6; MA G-GPE.B.6; NY GEO G.G-GPE.B.6. 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.148 Determine collinearity and parallelism from coordinates skill assessments:

Problem 1Difficulty: Mastery
A student claims that line p through (1, 2) and (4, 8) is parallel to line q through (-2, 5) and (4, 8) because their slopes, 2 and 1/2, are reciprocals. What is the best response?
AThe lines are parallel because reciprocal slopes always make parallel lines
BThe lines are parallel because both slopes are positive
CThe lines are not parallel because neither line is vertical
DThe lines are not parallel; parallel nonvertical lines must have equal slopes, and 2 is not equal to 1/2
Solution & Explanation:Slope p = (8 - 2)/(4 - 1) = 6/3 = 2. Slope q = (8 - 5)/(4 - (-2)) = 3/6 = 1/2. Parallel nonvertical lines need equal slopes, not reciprocal slopes, so the claim is incorrect.
Problem 2Difficulty: Mastery
Points A(-8, 10), B(-4, 7), C(0, 4), D(4, 1), and E(8, -3) are given. Which statement is correct?
AAll five points are collinear because the x-values increase by 4
BOnly D and E are collinear because their y-values are closest
CA, B, C, and D are collinear, but E is not on that same line
DNo three points are collinear because the y-values all change
Solution & Explanation:Slopes AB, BC, and CD are all -3/4. Slope DE is (-3 - 1)/(8 - 4) = -4/4 = -1, so E does not follow the same line as A, B, C, and D.
Problem 3Difficulty: Mastery
Which row of points represents a line parallel to a line with slope -3?
A(1, 4) and (3, 10)
B(0, 0) and (2, -6)
C(-2, 5) and (4, 3)
D(5, -1) and (5, -7)
Solution & Explanation:A line parallel to a line with slope -3 must also have slope -3. The correct row has slope (-6 - 0)/(2 - 0) = -6/2 = -3.

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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.B.5 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.5. Skill statement in this prompt cell: Select whether points are collinear or whether lines are parallel based on computed slopes or coordinate differences. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.B.5; FL MA.912.GR.3.3; MA G-GPE.B.5; TEKS §111.41(c); CCSS G-GPE.B.6; MA G-GPE.B.6; NY GEO G.G-GPE.B.6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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