Free Printable WorksheetMathGeometryMath CurriculumG-GPE.B.5

GEO.149 Determine perpendicularity from slopes or distances Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.149 Determine perpendicularity from slopes or distances. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.149 Determine perpendicularity from slopes or distances - 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 perpendicular based on their slopes (or coordinate information) and choose the supporting evidence. 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.149 Determine perpendicularity from slopes or distances skill assessments:

Problem 1Difficulty: Mastery
A coordinate figure has diamond ABCD with A(0,3), B(4,0), C(0,-3), and D(-4,0). Are diagonals AC and BD perpendicular?
AYes; AC is vertical and BD is horizontal.
BYes; both diagonals have slope 0.
CNo; AC is vertical, so it cannot be perpendicular to another line.
DNo; BD is horizontal, so it cannot be part of a perpendicular pair.
Solution & Explanation:Diagonal AC has constant x = 0, so it is vertical. Diagonal BD has constant y = 0, so it is horizontal. Vertical and horizontal lines are perpendicular.
Problem 2Difficulty: Mastery
Line l has direction change <9, -6>. Line m has direction change <2, 3>. Which slope evidence describes the relationship?
AThe lines are perpendicular because their slopes are -2/3 and 3/2.
BThe lines are parallel because 9 and 3 are multiples.
CThe lines are not perpendicular because the direction changes are not the same length.
DThe lines are perpendicular because both direction changes use positive x-values.
Solution & Explanation:A direction change <9, -6> gives slope -6/9 = -2/3. A direction change <2, 3> gives slope 3/2. Their product is -1.
Problem 3Difficulty: Mastery
Line a is ax + 6y = 12. Line b is 3x - 2y = 4. What value of a makes the two lines perpendicular?
Aa = -9
Ba = -4
Ca = 4
Da = 9
Solution & Explanation:Line a has slope -a/6. Line b has slope 3/2. For perpendicular lines, (-a/6)(3/2) = -1, which gives a = 4.

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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 perpendicular based on their slopes (or coordinate information) and choose the supporting evidence. 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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