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To perform a dilation of the points \( I(-2, -1) \), \( J(-2, 2) \), and \( K(2, 1) \) about the origin by a factor of 2.5, we will multiply both the \( x \)-coordinates and \( y \)-coordinates of each point by the dilation factor.

The dilation formula for a point \( (x, y) \) about the origin with a dilation factor \( k \) is:
\[
(x', y') = (k \cdot x, k \cdot y)
\]
where \( (x', y') \) is the new coordinate and \( k \) is the dilation factor.

Given \( k = 2.5 \), let's calculate the new coordinates:

1. **Point \( I(-2, -1) \)**:
   \[
   x' = 2.5 \cdot (-2) = -5, \quad y' = 2.5 \cdot (-1) = -2.5
   \]
   New point: \( I'(-5, -2.5) \)

2. **Point \( J(-2, 2) \)**:
   \[
   x' = 2.5 \cdot (-2) = -5, \quad y' = 2.5 \cdot 2 = 5
   \]
   New point: \( J'(-5, 5) \)

3. **Point \( K(2, 1) \)**:
   \[
   x' = 2.5 \cdot 2 = 5, \quad y' = 2.5 \cdot 1 = 2.5
   \]
   New point: \( K'(5, 2.5) \)

### Dilated Coordinates:
- \( I'(-5, -2.5) \)
- \( J'(-5, 5) \)
- \( K'(5, 2.5) \)

Would you like a detailed explanation of dilation or any further clarifications?

Here are 5 related questions you might find interesting:
1. How does the dilation factor affect the size of a shape?
2. What happens when the dilation factor is less than 1?
3. How would you dilate a shape about a point other than the origin?
4. Can dilation change the shape's orientation, or does it only affect size?
5. How would you calculate the area of a shape after dilation?

**Tip**: When performing dilations, the distance between any two points changes proportionally to the dilation factor, but their relative positions remain the same.

Dilation of 2.5 about the origin for points I(-2, -1), J(-2, 2), K(2, 1)

This problem involves performing a dilation of points I(-2, -1), J(-2, 2), and K(2, 1) by a factor of 2.5 about the origin. Learn how to apply the dilation formula to calculate new coordinates after transformation. Suitable for students in Grades 8-10 studying geometry and transformations.

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