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The problem asks for the image of the point \((2, 5)\) under a translation given by the rule \((x, y) \to (x+3, y-2)\).

We start with the point \((2, 5)\):
- The new \(x\)-coordinate will be \(2 + 3 = 5\),
- The new \(y\)-coordinate will be \(5 - 2 = 3\).

Thus, the image of the point \((2, 5)\) under the translation is \((5, 3)\).

The correct answer is \((5, 3)\), which corresponds to the green option.

Would you like any further details or explanations?

Here are 5 questions that build on this concept:
1. What is the image of the point \((4, 1)\) under the same translation \((x+3, y-2)\)?
2. How does a translation differ from a reflection?
3. If the translation rule was changed to \((x-2, y+4)\), what would the new image of \((2, 5)\) be?
4. Can a translation ever change the size or orientation of a figure?
5. What are the coordinates of the image of the origin \((0,0)\) under the translation \((x+3, y-2)\)?

**Tip:** A translation moves every point by the same distance in a given direction, keeping the shape and orientation of a figure intact.

What is the image of point (2,5) under the translation that shifts (x,y) to (x+3, y-2)?

Find the image of the point (2, 5) under the translation that shifts (x, y) to (x+3, y-2). This problem demonstrates the basic concept of translations in geometry, ideal for students in grades 6-8.

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