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.

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.

The keeper moves the entire feeding zone 6 units right and 3 units down.

What are the coordinates of A′? (, )

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)

For a different feeding schedule, rotate the original zone 90° clockwise about the origin.

What are the coordinates of C′? (, )

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)

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.

The plotted vertices outline a feeding zone. Dilate the zone by a scale factor of 2.

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

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)

The table shows corresponding vertices before and after a dilation centered at the origin.

Expanded Feeding Zone
Vertex	Original	Image
G	(−2, 1)	(−6, 3)
H	(1, 2)	(3, 6)
J	(2, −1)	(6, −3)

What is the scale factor?

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.

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.