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Water Quality Lab: Overlay Designs worksheet preview

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Water Quality Lab: Overlay Designs

Analyze water-quality lab diagrams using similarity, coordinate transformations, 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, Circle the answer, Short answer

About this worksheet

What students practice

  • Students identify similarity using rigid motions and dilations.
  • Students describe and complete transformation sequences between corresponding figures.
  • Students distinguish uniform scaling from changes that do not preserve shape.

How to use

Use after introducing similarity transformations. Have students sketch intermediate images on separate paper and explain how they check all corresponding vertices.

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.

Preview

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Water Quality Lab: Overlay Designs

Use transformations to compare sampling regions and lab diagrams.

Sampling Overlays

A community science lab uses overlays to mark regions in water-sample images. Corresponding vertices are listed in matching order. All scale factors are positive.

1.
Triangle ABC is a sampling region. The lab shrinks it by a factor of 1/2 centered at A. Which statement describes the image?−5−4−3−2−1123450−5−4−3−2−112345ABC
  • A. A stays at (−2, −2), and every side length is halved.
  • B. A moves to (−1, −1), and every side length is unchanged.
  • C. A moves to (−1, −1), and every side length is halved.
  • D. A stays at (−2, −2), and every side length is doubled.
2.
A four-sided sample boundary has vertices K(−4, 0), L(0, 0), M(0, 2), and N(−2, 4). The lab dilates it by 1/2 about the origin, then reflects it across the x-axis.

Write the coordinates of the image of N: ( ,  ).

3.
A lab report repositions and enlarges a sampling boundary. Which sequence maps every original vertex to its corresponding report vertex?
Sampling Boundary Coordinates
VertexOriginalReport
K(−1, 1)(−3, −3)
L(−1, 2)(−6, −3)
M(−3, 2)(−6, −9)
N(−2, 1)(−3, −6)
  • A. Rotate 90° clockwise, then dilate by 3, both about the origin.
  • B. Reflect across the x-axis, then dilate by 3 about the origin.
  • C. Rotate 180°, then dilate by 3, both about the origin.
  • D. Rotate 90° counterclockwise, then dilate by 3, both about the origin.

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