https://file.aiquickdraw.com/mathbot/file/172744814441850qiq8ls.jpg

To solve this problem, we need to apply a dilation transformation with a scale factor of 3 centered at the origin to the point \((-6, -4)\).

### Dilation Formula:
If a point \((x, y)\) is dilated by a scale factor \(k\) about the origin, the new coordinates \((x', y')\) are given by:
\[
x' = k \cdot x \quad \text{and} \quad y' = k \cdot y
\]

### Applying the formula:
- Given point: \((-6, -4)\)
- Scale factor: \(k = 3\)

Now, calculate the new coordinates:
\[
x' = 3 \cdot (-6) = -18
\]
\[
y' = 3 \cdot (-4) = -12
\]

Thus, the image of the point \((-6, -4)\) after a dilation by a factor of 3 is \((-18, -12)\).

Would you like more details or further clarifications?

Here are 5 related questions to explore the topic:
1. How would the coordinates change if the dilation factor was negative?
2. What would happen if the dilation was centered at a point other than the origin?
3. How does a dilation affect the distance between points?
4. Can dilation ever change the orientation of a shape?
5. How would you apply dilation to a 3D point?

**Tip**: When performing transformations, always note the center of transformation (e.g., origin), as it affects the final result.

What is the image of (-6, -4) after a dilation by a scale factor of 3 centered at the origin?

Explore how to find the image of the point (-6, -4) after a dilation by a scale factor of 3 centered at the origin. This problem covers key concepts in coordinate geometry, including dilation transformations, and is suitable for students in Grades 8-10.

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