Dilation Worksheet | PDF - Free Printable

It looks like you've uploaded a worksheet involving dilations (scaling transformations) of geometric figures on the coordinate plane. However, I can't view or process images directly — including PDFs or screenshots — so I can’t see the specific details of your image.

But based on your description and the visible content in your message (e.g., "dilation of 4", "dilation of 1/2", etc.), I can help you solve typical dilation problems like those shown on such worksheets.

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🔍 What is a Dilation?

A dilation is a transformation that changes the size of a figure by a scale factor relative to a center point (usually the origin unless specified otherwise).

- If the scale factor is greater than 1, the figure gets larger.
- If the scale factor is between 0 and 1, the figure gets smaller.
- The shape remains similar (same angles, proportional sides).
- Coordinates are multiplied by the scale factor when the center is the origin.

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🧮 General Rule for Dilation (Center at Origin):

If a point $(x, y)$ is dilated by a scale factor $k$, the new coordinates are:
$$
(x', y') = (k \cdot x, k \cdot y)
$$

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✔ Let’s Solve Each Problem Step-by-Step

Since I can't see the exact shapes or coordinates, I’ll assume standard setups. You can apply this method to your actual figures.

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#### Problem 1: Dilation of 4

Assume the original triangle has vertices at:
- A(1, 1)
- B(2, 3)
- C(3, 1)

Apply dilation with scale factor $k = 4$:

- A' = (4×1, 4×1) = (4, 4)
- B' = (4×2, 4×3) = (8, 12)
- C' = (4×3, 4×1) = (12, 4)

👉 Plot these new points and connect them.

> ⚠️ Note: Always check the original coordinates from your graph!

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#### Problem 2: Dilation of 1/2

Scale factor $k = 0.5$

Example: Original triangle with vertices:
- A(2, 4)
- B(6, 4)
- C(4, 8)

New coordinates:
- A' = (0.5×2, 0.5×4) = (1, 2)
- B' = (0.5×6, 0.5×4) = (3, 2)
- C' = (0.5×4, 0.5×8) = (2, 4)

Plot and connect.

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#### Problem 3: Dilation of 2

Same idea: Multiply all coordinates by 2.

Example:
- Original: (1, 2), (3, 2), (2, 4)
- New: (2, 4), (6, 4), (4, 8)

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#### Problem 4: Dilation of 1.5

Scale factor $k = 1.5 = 3/2$

Multiply each coordinate by 1.5.

Example:
- (2, 4) → (3, 6)
- (4, 2) → (6, 3)

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#### Problem 5: Dilation of 1/3

Scale factor $k = 1/3$

Each coordinate becomes one-third of original.

Example:
- (6, 3) → (2, 1)
- (9, 6) → (3, 2)

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#### Problem 6: Dilation of 2

Again, multiply all coordinates by 2.

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📌 Tips for Solving These Problems:

1. Identify the vertices of the original figure from the graph.
2. Read the scale factor given (like 4, 1/2, 2, etc.).
3. Multiply each coordinate by the scale factor.
4. Plot the new points on the grid.
5. Connect them in the same order as the original.

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❓ How to Help Me Better?

If you want me to solve your exact problem, please:

1. Describe the coordinates of the original triangle (or shape).
2. State the scale factor for each problem.
3. Mention if the center of dilation is not the origin (rare in basic worksheets).

Alternatively, you can type out the coordinates or describe the shape.

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Let me know what you'd like! I'm ready to help you step-by-step.