Students practice scaling geometric shapes like parallelograms and triangles on a coordinate grid using specific scale factors.

Since I can't view or access uploaded images directly, I can’t see the specific image you're referring to. However, based on your description, it appears to be a worksheet titled "Dilations on the Coordinate Plane" with four problems involving dilating geometric figures (a parallelogram, a kite, and two triangles) using different centers of dilation and scale factors.

Let me help you solve this type of problem step by step. If you provide the coordinates of the original points or describe the shapes and their positions, I can guide you through the solution. But for now, here's how to approach each problem:

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🔷 General Rule for Dilations:

A dilation is a transformation that changes the size of a figure by a scale factor from a center of dilation.

- If the center of dilation is at the origin (0, 0), then:
$$
(x, y) \rightarrow (kx, ky)
$$
where $ k $ is the scale factor.

- If the center of dilation is not at the origin, say at point $ (a, b) $, then:
$$
(x, y) \rightarrow (a + k(x - a), b + k(y - b))
$$

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Let’s go through each problem as described in your worksheet:

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✔ Problem 1: Dilate Parallelogram ABCD

- Center of dilation: (0, 0)
- Scale factor: 2

Steps:
1. Find the coordinates of A, B, C, D from the graph.
2. Multiply each coordinate by 2 (since scale factor = 2).
3. Plot the new points A', B', C', D'.

> Example: If A is at (1, 2), then A' = (2×1, 2×2) = (2, 4)

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✔ Problem 2: Dilate Kite EFGH

- Center of dilation: (0, 0)
- Scale factor: 2

Same process as above:
- Multiply each vertex’s x and y coordinates by 2.

> Example: If E is at (-2, 1), then E' = (-4, 2)

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✔ Problem 3: Dilate Triangle LJK

- Center of dilation: (0, 0)
- Scale factor: 1/2

Now we are shrinking the triangle by half.

- Multiply each coordinate by 0.5 (or divide by 2).

> Example: If L is at (6, 4), then L' = (3, 2)

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✔ Problem 4: Dilate Triangle LMN

- Center of dilation: (0, 0)
- Scale factor: 1/2

Again, shrink each coordinate by half.

> Example: If M is at (4, -2), then M' = (2, -1)

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📌 Final Steps:

For each problem:
1. Read the original coordinates from the graph.
2. Apply the dilation rule:
- If center is (0, 0): multiply both x and y by scale factor.
3. Write the new coordinates in the blanks provided.

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🔍 Example (if you had a point):

Suppose in Problem 1, point A is at (1, 3). Then:
- A' = (2×1, 2×3) = (2, 6)

Repeat for all points.

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⚠️ Important Note: Since I cannot see the actual image, I can't give exact coordinates. Please provide the coordinates of the original points, or describe the shape positions, and I’ll compute the dilated coordinates exactly.

Alternatively, if you can type out the coordinates of each point (like A(1,2), B(3,2), etc.), I can complete the entire worksheet for you.

Would you like to do that?