Dilation practice worksheet for students to graph dilated images of triangles on coordinate grids using specified scale factors.

Since I can’t view or process images directly, I’ll solve the problem based on your description — a “Dilation Practice” worksheet with 4 problems asking you to:

- For #1–4: Create a table of points for the pre-image (graphed), then graph the image given the scale factor.
- For #5–8: Complete the table of points for the pre-image and image (both graphed), then determine the scale factor.

I’ll walk through each of the four dilation problems as if I were doing the worksheet, assuming standard grid paper and common shapes. Since no actual coordinates are visible, I’ll assume typical starting points for each shape that would appear on such a worksheet. You can adjust the numbers if your image has different coordinates.

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## 🔷 Problem 1: Dilate by a factor of 0.5

Assumed Pre-Image Points (Triangle):

Let’s say the triangle has vertices at:
- A(2, -2)
- B(4, 0)
- C(6, -2)

*(This is a simple downward-pointing triangle centered around x=4, y=-2)*

Step 1: Multiply each coordinate by 0.5

New Image Points:
- A’ = (2×0.5, -2×0.5) = (1, -1)
- B’ = (4×0.5, 0×0.5) = (2, 0)
- C’ = (6×0.5, -2×0.5) = (3, -1)

Step 2: Graph the new triangle

Plot A’, B’, C’ — it will be half the size, centered at the same origin (if dilation is from origin).

> ✔ Table for #1:

| Pre-Image | Image (×0.5) |
|-----------|--------------|
| (2, -2) | (1, -1) |
| (4, 0) | (2, 0) |
| (6, -2) | (3, -1) |

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## 🔷 Problem 2: Dilate by a factor of 1/4

Assumed Pre-Image Points (Right Triangle):

Vertices:
- D(4, 2)
- E(4, 6)
- F(8, 2)

*(Right triangle with right angle at D, going up and right)*

Step 1: Multiply each coordinate by 1/4 = 0.25

New Image Points:
- D’ = (4×0.25, 2×0.25) = (1, 0.5)
- E’ = (4×0.25, 6×0.25) = (1, 1.5)
- F’ = (8×0.25, 2×0.25) = (2, 0.5)

Step 2: Graph the smaller triangle

Much smaller, still right-angled, same orientation.

> ✔ Table for #2:

| Pre-Image | Image (×0.25) |
|-----------|---------------|
| (4, 2) | (1, 0.5) |
| (4, 6) | (1, 1.5) |
| (8, 2) | (2, 0.5) |

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## 🔷 Problem 3: Dilate by a factor of 1.5

Assumed Pre-Image Points (Parallelogram):

Vertices:
- G(2, 1)
- H(4, 3)
- I(6, 1)
- J(4, -1)

*(Diamond-like parallelogram centered at (4,1))*

Step 1: Multiply each coordinate by 1.5

New Image Points:
- G’ = (2×1.5, 1×1.5) = (3, 1.5)
- H’ = (4×1.5, 3×1.5) = (6, 4.5)
- I’ = (6×1.5, 1×1.5) = (9, 1.5)
- J’ = (4×1.5, -1×1.5) = (6, -1.5)

Step 2: Graph the larger parallelogram

Stretched by 50%, same center point if dilating from origin.

> ✔ Table for #3:

| Pre-Image | Image (×1.5) |
|-----------|--------------|
| (2, 1) | (3, 1.5) |
| (4, 3) | (6, 4.5) |
| (6, 1) | (9, 1.5) |
| (4, -1) | (6, -1.5) |

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## 🔷 Problem 4: Dilate by a factor of 2.5

Assumed Pre-Image Points (Small Triangle):

Vertices:
- K(1, 1)
- L(2, 3)
- M(3, 1)

*(Small upward-pointing triangle)*

Step 1: Multiply each coordinate by 2.5

New Image Points:
- K’ = (1×2.5, 1×2.5) = (2.5, 2.5)
- L’ = (2×2.5, 3×2.5) = (5, 7.5)
- M’ = (3×2.5, 1×2.5) = (7.5, 2.5)

Step 2: Graph the much larger triangle

Expanded significantly — note fractional coordinates may need careful plotting.

> ✔ Table for #4:

| Pre-Image | Image (×2.5) |
|-----------|--------------|
| (1, 1) | (2.5, 2.5) |
| (2, 3) | (5, 7.5) |
| (3, 1) | (7.5, 2.5) |

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## 🧠 How to Solve Problems #5–8 (If You Had Them):

These ask you to find the scale factor, given both pre-image and image points.

Example Method:

Suppose you’re given:
- Pre-image point: (2, 4)
- Image point: (6, 12)

→ Scale factor = 6 ÷ 2 = 3, or 12 ÷ 4 = 3 → Scale factor = 3

Check multiple points to confirm consistency.

> ⚠️ Important: All corresponding points must have the *same* scale factor for a valid dilation.

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## 📌 Key Concepts Recap:

- Dilation: Transformation that enlarges or reduces a figure by a scale factor from a center point (usually origin unless specified).
- Scale Factor > 1: Enlargement
- Scale Factor < 1: Reduction
- Scale Factor = 1: No change
- To find image: Multiply each coordinate of pre-image by scale factor.
- To find scale factor: Divide image coordinate by pre-image coordinate (for same point).

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✔ Final Tip for Worksheet:
Always label your tables clearly and plot points accurately. Use a ruler for straight lines. If the dilation is not from the origin, you’d need to translate first — but most middle/high school worksheets assume dilation from origin unless stated otherwise.

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If you can describe the actual coordinates from your image (e.g., “the triangle has points at (0,0), (2,0), (1,2)”), I can give you exact answers for your specific worksheet!

Let me know if you want help with problems #5–8 too — just provide the pre-image and image points!