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Level Studio: Fair-Play Shape Checks

Verify congruent game-level regions, track rigid-motion sequences, and explain how matching outlines supports fair level design.

Grade 8MathInteractive · Printable

Aligned to8.G.A.2

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What’s included

Single worksheet
Auto-graded online
1 Common Core standard
Printable answer key
13 questions
Classroom-ready

Details

Format: Interactive · Printable
Grade: Grade 8
Subject: Math
Question types: Fill in the blank, Multiple choice, Circle the answer, Short answer, Drawing

About this worksheet

What students practice

Students verify congruence by identifying sequences of rotations, reflections, and translations.
Students describe and track rigid-motion sequences using corresponding vertices.
Students distinguish evidence of congruence from matching game scores or incomplete shape checks.

How to use

Use after introducing coordinate transformations. Have students trace outlines or record intermediate coordinates, then discuss the final fairness check.

Curriculum

Common Core standard covered

8.G.A.2

Understand congruent figures as ones linked by rotations, reflections, and translations, and describe such a sequence.

Preview

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Level Studio: Fair-Play Shape Checks

Use rigid motions to compare level regions and score-zone outlines.

Check the Level Regions

A game studio is balancing levels and scores. Its collision regions are the shapes that register contact with a player. Compare outlines, not their point values. All coordinates use grid units.

Two bonus regions each award 80 points. Which additional fact proves that their outlines are congruent?

A. Both outlines enclose the same area.
B. A rigid-motion sequence matches the entire outlines.
C. Both outlines have the same perimeter.
D. Both outlines have the same number of vertices.

The studio copies collision region ABCD, whose boundary follows A–B–C–D–A, into another level. Its target vertices are P(1, 1), Q(4, 1), R(3, −1), and S(1, 0). Which sequence maps A → P, B → Q, C → R, and D → S?

A. Reflect across the y-axis; translate 5 units right and 1 unit up.
B. Reflect across the y-axis; translate 5 units right and 1 unit down.
C. Reflect across the x-axis; translate 5 units left and 1 unit up.
D. Reflect across the x-axis; translate 5 units right and 1 unit up.

A score-zone corner starts at (3, −2). The entire zone rotates 90° counterclockwise about the origin, reflects across the x-axis, and then translates 4 units left and 1 unit up.

Write the corner's final coordinates: ( , ).

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