Free Printable WorksheetMathGeometryMath CurriculumG-GPE.B.4

GEO.139 Distance from a point to a line and between parallel lines Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.139 Distance from a point to a line and between parallel lines. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.139 Distance from a point to a line and between parallel lines - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.4. Skill statement in this prompt cell: Select the correct setup to compute the distance from a point to a line (or between parallel lines) and choose the correct distance. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.B.4; FL MA.912.GR.3.2-3.3; MA G-GPE.B.4; NY GEO G.G-GPE.B.4; CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1. 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.139 Distance from a point to a line and between parallel lines skill assessments:

Problem 1Difficulty: Mastery
The graph shows two lane-marker lines modeled by 20x + 21y - 42 = 0 and 20x + 21y + 45 = 0. Which setup and exact distance correctly find the lane spacing?
Aabs(45 - (-42))/(20+21) = 87/41 units
Babs(45 - (-42))/sqrt((20)2+(21)2) = 3 units
Cabs(45 + (-42))/sqrt((20)2+(21)2) = 3/29 units
Dabs(45 - (-42))/sqrt(20+21) = 87/sqrt(41) units
Solution & Explanation:For parallel lines written with the same A and B, use |C2 - C1|/sqrt(A2 + B2). Here the constant difference is |45 - (-42)| = 87, and sqrt(400+441) = sqrt(841), so the distance is 3 units.
Problem 2Difficulty: Mastery
The parallel lines are y = (5/2)x + 1 and y = (5/2)x - 8. Which setup and distance correctly find the perpendicular distance between them?
Aabs(-8 - (1)) = 9 units
Babs(-16 - (2))/(5+2) = 18/7 units
Cabs(-16 - (2))/sqrt((5)2+(-2)2) = 18/sqrt(29) units
Dabs(-16 + (2))/sqrt((5)2+(-2)2) = 14/sqrt(29) units
Solution & Explanation:Convert the equations to matching standard form: 5x - 2y + 2 = 0 and 5x - 2y - 16 = 0. The constant difference is 18, and sqrt(A2 + B2) = sqrt(29), so the distance is 18/sqrt(29) units.
Problem 3Difficulty: Mastery
For point P(-1, 2), the line 9x + 12y + h = 0 is 4 units away. Which value or values of h satisfy the condition?
Ah = 4 or h = -4
Bh = 60 or h = -60
Ch = -45 or h = 75
Dh = 45 or h = -75
Solution & Explanation:Use |9(-1) + 12(2) + h|/sqrt(92 + 122) = 4. This gives |15 + h|/15 = 4, so |15 + h| = 60 and h = 45 or h = -75.

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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.4 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.4. Skill statement in this prompt cell: Select the correct setup to compute the distance from a point to a line (or between parallel lines) and choose the correct distance. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.B.4; FL MA.912.GR.3.2-3.3; MA G-GPE.B.4; NY GEO G.G-GPE.B.4; CCSS G-MG.A.1; SMP.4; NY HS Modeling; MA G-MG.A.1. Use this prompt-provided wording as the supporting standard description for this workflow.).

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