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The question asks for the coordinates of the image of point \( L(-2, 5) \) after a dilation with a center at \( (0, 0) \) and a scale factor of 4.

To solve this:

1. The formula for dilation with a center at the origin is \( (x', y') = (kx, ky) \), where \( k \) is the scale factor, and \( (x, y) \) are the original coordinates.

2. For point \( L(-2, 5) \):
   - Apply the scale factor of 4 to the \( x \)- and \( y \)-coordinates:
   \[
   x' = 4 \times (-2) = -8
   \]
   \[
   y' = 4 \times 5 = 20
   \]
   So, the new coordinates of the image of \( L \) are \( (-8, 20) \).

This would be the image of point \( L \) after the dilation.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. How do you apply a dilation to points not centered at the origin?
2. What happens to the distance between points after a dilation with a certain scale factor?
3. How does a dilation affect the slope of a line?
4. What would happen if the scale factor was less than 1?
5. How would the dilation change if the center of dilation were not the origin?

**Tip:** When dilating points, always multiply both the \( x \)- and \( y \)-coordinates by the scale factor, and ensure the center of dilation is taken into account.

What are the coordinates of the image of L for a dilation with center (0, 0) and scale factor 4?

Learn how to find the image of point L(-2, 5) after a dilation with a center at (0, 0) and a scale factor of 4. This problem covers key geometric concepts related to dilations, transformations, and scaling. Suitable for students in Grades 8-10.

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