Dilations (A) Worksheet | Fun and Engaging 8th Grade PDF Worksheets - Free Printable

Let's solve this step-by-step. The task is to draw dilations (enlargements) of the given shapes using the specified scale factors on the grid.

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🔍 What is a Dilation?

A dilation is a transformation that changes the size of a shape by a scale factor, while keeping its shape and orientation the same. The dilation is centered at a point (often the origin or a corner of the shape), and each point of the shape is moved away from or toward that center by the scale factor.

In this worksheet, we assume the center of dilation is at the bottom-left corner of each shape, unless otherwise indicated. Since no center is specified, we'll use the bottom-left vertex as the reference point for scaling.

We will:
1. Measure the dimensions of the original shape.
2. Multiply each dimension by the scale factor.
3. Draw the new shape accordingly on the grid.

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✔ Step-by-Step Solutions

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#### 🔹 1. Top Left: Rectangle – Scale Factor 2

- Original rectangle: 3 units wide × 1 unit tall
- Scale factor = 2 → New dimensions:
- Width: 3 × 2 = 6 units
- Height: 1 × 2 = 2 units
- Draw a rectangle 6 units wide and 2 units tall, starting from the same bottom-left corner.

✔ Result: A larger rectangle twice as long and twice as tall.

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#### 🔹 2. Top Right: Rectangle – Scale Factor 3

- Original rectangle: 3 units wide × 1 unit tall
- Scale factor = 3 →
- Width: 3 × 3 = 9 units
- Height: 1 × 3 = 3 units
- Draw a rectangle 9 units wide and 3 units tall, from the same corner.

✔ Result: Three times larger in both directions.

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#### 🔹 3. Middle Left: Right Triangle – Scale Factor 2

- Original triangle: Base = 2 units, Height = 2 units
- Scale factor = 2 →
- Base: 2 × 2 = 4 units
- Height: 2 × 2 = 4 units
- Draw a right triangle with base and height of 4 units, maintaining the same angle and position relative to the bottom-left corner.

✔ Result: Larger triangle, twice the size.

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#### 🔹 4. Middle Right: Right Triangle – Scale Factor 3

- Original: Base = 2 units, Height = 2 units
- Scale factor = 3 →
- Base: 2 × 3 = 6 units
- Height: 2 × 3 = 6 units
- Draw triangle with base and height of 6 units.

✔ Result: Three times larger.

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#### 🔹 5. Bottom Left: L-Shaped Figure – Scale Factor 3

- Original L-shape: Made of 3 squares — vertical arm: 2 units high, horizontal arm: 2 units wide (with one shared square)
- So it’s like a 2×2 square missing one corner square.
- But let's break it down:
- Vertical part: 2 units up
- Horizontal part: 2 units right
- Scale factor = 3 →
- Each side becomes 3× longer
- So vertical arm: 2 × 3 = 6 units
- Horizontal arm: 2 × 3 = 6 units
- Draw an L-shape with:
- A vertical column of 6 squares
- A horizontal row of 6 squares extending from the bottom-right of the vertical column
- The "corner" where they meet remains the same

✔ Result: Enlarged L-shape, three times bigger.

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#### 🔹 6. Bottom Right: L-Shaped Figure – Scale Factor 4

- Same original shape as above
- Scale factor = 4 →
- Vertical arm: 2 × 4 = 8 units
- Horizontal arm: 2 × 4 = 8 units
- Draw an L-shape with:
- Vertical column of 8 squares
- Horizontal row of 8 squares from the bottom-right of the vertical arm

✔ Result: Four times larger.

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📌 Summary of How to Draw:

For each shape:
1. Identify the bottom-left corner as the center of dilation.
2. Measure the width and height of the shape.
3. Multiply each dimension by the scale factor.
4. Draw the new shape with those scaled dimensions, keeping the same orientation.

> ⚠️ Remember: All angles stay the same, only sizes change.

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✔ Final Answer (What You Should Draw):

| Shape | Scale Factor | New Dimensions |
|-------|--------------|----------------|
| Top-left rectangle | 2 | 6×2 |
| Top-right rectangle | 3 | 9×3 |
| Middle-left triangle | 2 | base=4, height=4 |
| Middle-right triangle | 3 | base=6, height=6 |
| Bottom-left L-shape | 3 | arms = 6 units |
| Bottom-right L-shape | 4 | arms = 8 units |

Draw each of these enlarged shapes starting from the same corner as the original.

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Since I can't draw directly here, you can now complete the worksheet by:
- Using a ruler to measure and extend the sides.
- Counting grid squares carefully.
- Keeping the shape aligned with the original.

Let me know if you'd like a visual guide or a printable version!