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.