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To perform a dilation of the given vertices by a scale factor of 5 centered at the origin, we will multiply the coordinates of each vertex by the scale factor.

The original coordinates of the vertices are:
- \( S ( -2, -2 ) \)
- \( T ( -2, 2 ) \)
- \( U ( 2, 2 ) \)
- \( V ( 2, -2 ) \)

To find the new coordinates after the dilation, we multiply each coordinate by 5:

1. \( S' = (-2 \times 5, -2 \times 5) = (-10, -10) \)
2. \( T' = (-2 \times 5, 2 \times 5) = (-10, 10) \)
3. \( U' = (2 \times 5, 2 \times 5) = (10, 10) \)
4. \( V' = (2 \times 5, -2 \times 5) = (10, -10) \)

Thus, the new coordinates of the vertices after the dilation are:
- \( S' (-10, -10) \)
- \( T' (-10, 10) \)
- \( U' (10, 10) \)
- \( V' (10, -10) \)

Would you like further clarification or details on this process?

Here are 5 questions related to dilation and transformations:
1. What happens to the shape of the figure after dilation?
2. How do different scale factors affect the size of the dilated figure?
3. What would the coordinates be if the scale factor was less than 1?
4. How is dilation different from translation or rotation?
5. How do you determine the center of dilation in a geometric transformation?

**Tip:** In dilation, the shape remains similar to the original, but the size changes according to the scale factor.

Write the coordinates of the vertices after a dilation with a scale factor of 5, centered at the origin.

Learn how to dilate a figure centered at the origin with a scale factor of 5. The original coordinates of the vertices are scaled by multiplying them by 5, transforming the figure. This problem covers geometric transformations, specifically dilation, and is suitable for students in Grades 8-10.

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