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Fish Tank Feeding Maps worksheet preview

Worksheet

Fish Tank Feeding Maps

Describe translations, reflections, rotations, and dilations using coordinate maps of aquarium feeding zones.

Grade 8MathInteractive · Printable

Aligned to8.G.A.3

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What’s included

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

Details

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

About this worksheet

What students practice

  • Students find image coordinates after translations, reflections, rotations, and dilations.
  • Students identify transformation rules and describe the effects of transformation order.

How to use

Use after introducing coordinate transformation rules. Have students mark image points on the maps as scratch work, then compare their rules and reasoning.

Curriculum

Common Core standard covered

8.G.A.3

Use coordinates to describe how dilations, translations, rotations, and reflections change 2-D figures.

Preview

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Name Date

Fish Tank Feeding Maps

Use coordinates to track feeding zones through geometric transformations.

Morning Feeding Maps

Coordinates show positions on a top-view tank map, not feeding times. A prime mark (′) names an image point. Use the stated transformation for each question.

−8−6−4−224680−8−7−6−5−4−3−2−112345678ABC
Points A, B, and C are the vertices of the morning triangular feeding zone. Use this map for Questions 1–4. Start with the original zone each time.
1.
The keeper moves the entire feeding zone 6 units right and 3 units down.

What are the coordinates of A′? ( ,  )

2.
A second tank uses a mirror image of the feeding zone across the y-axis. What are the image coordinates?
  • A. A′(2, −5), B′(2, −2), C′(5, −3)
  • B. A′(5, 2), B′(2, 2), C′(3, 5)
  • C. A′(5, −2), B′(2, −2), C′(3, −5)
  • D. A′(−5, −2), B′(−2, −2), C′(−3, −5)
3.
For a different feeding schedule, rotate the original zone 90° clockwise about the origin.

What are the coordinates of C′? ( ,  )

4.
Which rule moves B to (1, 6) and moves every other vertex by the same translation?
  • A. (x, y) → (x + 3, y + 4)
  • B. (x, y) → (x + 1, y + 6)
  • C. (x, y) → (x + 4, y + 3)
  • D. (x, y) → (x − 3, y + 4)
5.
A rectangular feeding zone has vertices (−4, 1), (−1, 1), (−1, 3), and (−4, 3). Its image has corresponding vertices (−4, −1), (−1, −1), (−1, −3), and (−4, −3). Which transformation produces this image?
  • A. Rotate the zone 180° about the origin.
  • B. Reflect the zone across the x-axis.
  • C. Translate the zone 2 units down.
  • D. Reflect the zone across the y-axis.

Resizing and Turning Zones

Use corresponding vertices to describe each change. Unless another center is stated, dilations and rotations are centered at the origin.

6.
The plotted vertices outline a feeding zone. Dilate the zone by a scale factor of 2.−8−6−4−224680−8−7−6−5−4−3−2−112345678DEF

What are the coordinates of D′? ( ,  ). What is the y-coordinate of F′?  

7.
A smaller tank needs a feeding zone that is a dilation of the original zone by a scale factor of 1/2. Which rule should the keeper use?
  • A. (x, y) → (x/2, y/2)
  • B. (x, y) → (2x, 2y)
  • C. (x, y) → (x/2, y)
  • D. (x, y) → (x − 1/2, y − 1/2)
8.
The table shows corresponding vertices before and after a dilation centered at the origin.
Expanded Feeding Zone
VertexOriginalImage
G(−2, 1)(−6, 3)
H(1, 2)(3, 6)
J(2, −1)(6, −3)

What is the scale factor?  

9.
A triangular zone has vertices K(−4, −1), L(−2, −1), and M(−2, 3). Rotate it 90° counterclockwise about the origin. Where is K′?
  • A. K′(−4, 1)
  • B. K′(−1, 4)
  • C. K′(1, −4)
  • D. K′(4, 1)
10.
A feeding zone is dilated by a scale factor of 2 with center (1, 1), rather than the origin. One vertex is P(−2, 3).

What are the coordinates of P′? ( ,  )

Afternoon Schedule Checks

Apply transformations in the order stated. Check both coordinates when reviewing a keeper's work.

11.
At noon, the triangular zone shown is reflected across the x-axis. At 3 p.m., that image is translated 2 units left.−7−6−5−4−3−2−112345670−7−6−5−4−3−2−11234567RST

What are the final coordinates of S? ( ,  )

12.
A keeper rotates a feeding zone 180° about the origin, then dilates the image by a scale factor of 1/2 centered at the origin. Which rule describes the combined change?
  • A. (x, y) → (−x/2, y/2)
  • B. (x, y) → (−2x, −2y)
  • C. (x, y) → (y/2, −x/2)
  • D. (x, y) → (−x/2, −y/2)
13.
Before a feeding zone was translated 5 units right and 2 units down, one vertex was W. After the translation, its image was W′(2, −6).

What were the original coordinates of W? ( ,  )

14.
Nia says, “For a feeding zone, translating 3 units right and then reflecting across the y-axis gives the same result as reflecting across the y-axis and then translating 3 units right.” Test her claim using the vertex V(−2, 1). Give its final coordinates for each order and explain whether her claim is correct.

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