Free Printable WorksheetMathGeometryMath CurriculumG-GPE.B.5

GEO.138 Parallel and perpendicular lines in the coordinate plane Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.138 Parallel and perpendicular lines in the coordinate plane. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.138 Parallel and perpendicular lines in the coordinate plane - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.5. Skill statement in this prompt cell: Select whether two lines are parallel or perpendicular based on slope and choose the correct equation of a parallel or perpendicular line through a point. 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). 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.138 Parallel and perpendicular lines in the coordinate plane skill assessments:

Problem 1Difficulty: Mastery
A graph shows station S(-4, 2). An existing route has equation 2x + y = 3. Which endpoint E would make segment SE perpendicular to the existing route?
AE(0, 4)
BE(2, -1)
CE(-2, 6)
DE(4, 0)
Solution & Explanation:The existing route has slope -2, so a perpendicular segment must have slope 1/2. The slope from S(-4, 2) to E(0, 4) is (4 - 2)/(0 - (-4)) = 1/2.
Problem 2Difficulty: Mastery
Line r has equation y = mx + 4 and passes through (-2, 1). Line s must be perpendicular to r and pass through (6, -1). Which equation is line s?
Ay = 3/2x - 10
By = -2/3x + 3
Cy = 2/3x - 5
Dy = -3/2x + 8
Solution & Explanation:Use (-2, 1) in y = mx + 4: 1 = -2m + 4, so m = 3/2. A perpendicular line has slope -2/3. Through (6, -1), the equation is y = -2/3x + 3.
Problem 3Difficulty: Mastery
Which pair of points could define a line parallel to 7x - 2y = 4?
A(-3, -5) and (1, 9)
B(-3, 9) and (1, -5)
C(-3, -5) and (1, -3)
D(-3, 5) and (1, 9)
Solution & Explanation:The equation 7x - 2y = 4 has slope 7/2. The slope through (-3, -5) and (1, 9) is (9 - (-5))/(1 - (-3)) = 14/4 = 7/2, so it is parallel.

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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.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 two lines are parallel or perpendicular based on slope and choose the correct equation of a parallel or perpendicular line through a point. 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). Use this prompt-provided wording as the supporting standard description for this workflow.).

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