Transformations and Similarity

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📐 Part 1: Similarity and Scale Factor

1. Triangle ABC has side lengths of 6, 8, and 10 inches. If it's scaled by a factor of 1.5, what are the new side lengths?

New side lengths: _______ inches, _______ inches, _______ inches

2. A playground blueprint uses a scale factor of 1:50. If a slide is 2 inches on the blueprint, how long is the actual slide?

25 feet

100 inches

8 feet 4 inches

50 inches

3. If a rectangle has an area of 24 square units and is dilated by a scale factor of 3, what is the new area?

New area: _______ square units

4. Two similar triangles have corresponding sides in the ratio 2:5. If the smaller triangle has a perimeter of 18 cm, what is the perimeter of the larger triangle?

Larger triangle perimeter: _______ cm

🔄 Part 2: Coordinate Transformations

5. Point A is located at (4, -2). After a translation of 3 units right and 5 units up, what are the new coordinates?

New coordinates: ( _____ , _____ )

6. Which transformation rule represents a reflection over the y-axis?

(x, y) → (-x, y)

(x, y) → (x, -y)

(x, y) → (-x, -y)

(x, y) → (y, x)

7. Point B(6, 3) is rotated 90° counterclockwise around the origin. What are the new coordinates?

New coordinates: ( _____ , _____ )

8. A triangle has vertices at A(2, 1), B(4, 1), and C(3, 4). After a rotation of 180° around the origin, list the new coordinates:

A': ( _____ , _____ ) B': ( _____ , _____ ) C': ( _____ , _____ )

🏗️ Part 3: Real-World Applications

9. An architect is designing a park layout on a coordinate grid. She places a fountain at (0, 0) and wants to place identical flower beds at symmetric locations. If one flower bed is at (8, 6), where should she place the other three to create a symmetric design?

10. A video game designer needs to create multiple sizes of the same character sprite. The original character is 32 pixels tall. If the designer wants versions that are 75% and 150% of the original size, what heights should the new sprites be?

75% size: _______ pixels tall

150% size: _______ pixels tall

11. Explain in your own words: How do transformations help architects and designers in their work? Give at least one specific example.

Transformations and Similarity

Transformations and Similarity

📐 Part 1: Similarity and Scale Factor

🔄 Part 2: Coordinate Transformations

🏗️ Part 3: Real-World Applications

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