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Recycling Drive: Sign Design Sequences

Analyze recycling-drive sign designs using coordinate diagrams, similarity, and sequences of rigid motions and dilations.

Grade 8MathInteractive · Printable

Aligned to8.G.A.4

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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, Matching, Circle the answer, Short answer

About this worksheet

What students practice

Students identify sequences of rigid motions and dilations that map corresponding vertices.
Students use corresponding lengths and angles to evaluate similarity claims.
Students describe how dilation centers affect the positions of similar figures.

How to use

Use after introducing similarity transformations. Have students record intermediate coordinates on separate paper and justify the final similarity claim.

Curriculum

Common Core standard covered

8.G.A.4

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

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Recycling Drive: Sign Design Sequences

Use transformations to compare signs for cans, bottles, and paper.

Track the Design Stages

Each outline belongs to a recycling-drive sign. Follow transformations in the stated order. All scale factors are positive.

The cans sign uses triangle ABC. First translate it 4 units right and 3 units up. Next perform a rotation about the origin. Finally dilate by 2 about the origin. The target vertices are P(0, 0), Q(0, 6), and R(−4, 0), with A → P, B → Q, and C → R. Which rotation completes this sequence?

A. Rotate 180°.
B. Rotate 90° clockwise.
C. Rotate 90° counterclockwise.
D. Rotate 360°.

A paper-collection sign is reflected across the vertical line x = 1, then dilated by 3 about the origin. Reflection across x = 1 places each point the same horizontal distance on the opposite side of that line. One original corner is (−1, 2).

Find the final coordinates of this corner: ( , ).

A bottle-collection marker has A(1, −2), B(3, −2), and C(1, −1). Match each editing plan to its final vertices, listed in the order A, B, C. Every rotation and dilation is centered at the origin.