https://file.aiquickdraw.com/mathbot/file/17256485991034wmyit8d.jpg

The image shows a rectangular figure on a coordinate plane, and the problem asks for the coordinates of the vertices after a dilation with a scale factor of 5 about the origin. Let's proceed with solving the problem step by step.

### Step 1: Identify the current coordinates of the vertices
From the image, the coordinates of the vertices appear to be:
- \( C(-2, 2) \)
- \( D(2, 2) \)
- \( F(2, -2) \)
- \( B(-2, -2) \)

### Step 2: Apply the dilation formula
The formula for dilation about the origin with a scale factor \( k \) is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
Given the scale factor \( k = 5 \), we will multiply each vertex's coordinates by 5.

### Step 3: Find the new coordinates after dilation
1. For vertex \( C(-2, 2) \):
\[
C' = (5 \cdot (-2), 5 \cdot 2) = (-10, 10)
\]

2. For vertex \( D(2, 2) \):
\[
D' = (5 \cdot 2, 5 \cdot 2) = (10, 10)
\]

3. For vertex \( F(2, -2) \):
\[
F' = (5 \cdot 2, 5 \cdot (-2)) = (10, -10)
\]

4. For vertex \( B(-2, -2) \):
\[
B' = (5 \cdot (-2), 5 \cdot (-2)) = (-10, -10)
\]

### Final Coordinates after Dilation:
- \( C'(-10, 10) \)
- \( D'(10, 10) \)
- \( F'(10, -10) \)
- \( B'(-10, -10) \)

These are the new coordinates of the vertices after dilation.

Would you like further details or have any questions? Here are some related questions to practice:

1. What happens to the area of the figure after the dilation with a scale factor of 5?
2. How would the coordinates change if the scale factor was \(-5\) instead of 5?
3. How do you determine the center of dilation from a transformation?
4. How would a translation affect the dilated image?
5. What would be the result of applying a reflection after dilation?

**Tip:** Dilation enlarges or reduces the size of a figure, but preserves its shape and orientation if the scale factor is positive.

Write the coordinates of the vertices after a dilation with a scale factor of 5 about the origin.

This problem involves dilating a rectangle on the coordinate plane using a scale factor of 5 about the origin. Learn how to apply the dilation formula to find the new coordinates of the vertices, suitable for students in Grades 8-10.

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