Free Printable WorksheetMathGrade 8Math Curriculum8.G.A.2

8.118 Describing a Sequence of Transformations for Congruence Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.118 Describing a Sequence of Transformations for Congruence. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.118 Describing a Sequence of Transformations for Congruence - Which sequence of rigid motions correctly maps the preimage onto the congruent image? (CCSS 8.G.A.2; CA 8.G.A.2; MA 8.G.A.2)

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

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

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Below are sample questions representative of the exercises included on this worksheet and related 8.118 Describing a Sequence of Transformations for Congruence skill assessments:

Problem 1Difficulty: Hard
Consider triangle UVW with vertices U(1, -4), V(3, 1), and W(-2, 0). The corresponding image is triangle U'V'W' with vertices U'(2, 8), V'(4, 3), and W'(-1, 4). A reflection across y = k followed by translating 1 unit right maps the preimage to the image. What is k?
Solution & Explanation:Start with U(1, -4). After reflecting across y = 2, it is at (1, 8). Then translating 1 unit right moves it to (2, 8), which matches U'. So the line of reflection is y = 2.
Problem 2Difficulty: Hard
Consider pentagon ABCDE with vertices A(-2, -3), B(-1, -4), C(1, -3), D(3, 0), and E(-1, 0). The corresponding image is pentagon A'B'C'D'E' with vertices A'(1, 5), B'(2, 6), C'(4, 5), D'(6, 2), and E'(2, 2). A reflection across y = k followed by translating 3 units right maps the preimage to the image. What is k?
Solution & Explanation:Start with B(-1, -4). After reflecting across y = 1, it is at (-1, 6). Then translating 3 units right moves it to (2, 6), which matches B'. So the line of reflection is y = 1.
Problem 3Difficulty: Hard
pentagon RSTUV with vertices R(-2, -2), S(3, -2), T(2, 2), U(-2, 3), and V(-3, 3). A matching congruent figure is pentagon R'S'T'U'V' with vertices R'(-1, 1), S'(-1, -4), T'(-5, -3), U'(-6, 1), and V'(-6, 2). Before the final translation, apply this sequence: Reflect across the line y = -2, then rotate 90 degrees clockwise about the origin. What is the y-value of the translation that reaches the image?
Solution & Explanation:Start with T(2, 2). After reflecting across the line y = -2, it is at (2, -6). After rotating 90 degrees clockwise about the origin, it is at (-6, -2). To reach T'(-5, -3), the y-coordinate must change by -1. So the required vertical shift is -1.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.G.A.2 (Primary standard selected for prompt fields: CCSS 8.G.A.2. Skill statement: Which sequence of rigid motions correctly maps the preimage onto the congruent image? Associated standards listed with this skill: CCSS 8.G.A.2; CA 8.G.A.2; MA 8.G.A.2. Use this embedded wording as the best available supporting standard description for this workflow.).

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