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.