https://file.aiquickdraw.com/mathbot/file/1729176827928us5oumt8.jpg

The problem provides that the point \((1, 1)\) is translated to \((0, 3)\). This gives us the translation rule:

\[
(x', y') = (x + \Delta x, y + \Delta y)
\]
Where \((\Delta x, \Delta y)\) is the translation vector.

To find \(\Delta x\) and \(\Delta y\):
- From \((1, 1)\) to \((0, 3)\):
\[
\Delta x = 0 - 1 = -1 \quad \text{and} \quad \Delta y = 3 - 1 = 2
\]
Thus, the translation vector is \((-1, 2)\).

Now, we apply this same translation to the point \((-4, -1)\):
\[
x' = -4 + (-1) = -5 \quad \text{and} \quad y' = -1 + 2 = 1
\]

Therefore, the coordinates of the image of the point \((-4, -1)\) under the same translation are \((-5, 1)\).

Do you want more details or have any questions?

Here are 5 follow-up questions for further practice:
1. How would the translation change if the point \((1, 1)\) was translated to \((2, 2)\)?
2. Can you describe what happens geometrically when a point undergoes translation?
3. What is the image of the point \((3, -2)\) under the translation \((-2, 5)\)?
4. How do you derive a translation vector from two given points?
5. What happens to the coordinates of a point if it is translated by the vector \((0, 0)\)?

**Tip**: Always double-check your arithmetic when working with translations to avoid simple errors.

The image of the point (1, 1) under a translation is (0, 3). Find the coordinates of the image of the point (-4, -1) under the same translation.

This problem involves finding the image of a point under a translation. Given that the point (1, 1) is translated to (0, 3), we determine the image of (-4, -1) under the same translation using the concept of translation vectors. Perfect practice for students in Grades 8-10.

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