The image of the point left parenthesis, 2, comma, minus, 9, right parenthesis(2,−9) under a translation is left parenthesis, 4, comma, minus, 14, right parenthesis(4,−14). Find the coordinates of the image of the point left parenthesis, 5, comma, 6, right parenthesis(5,6) under the same translation

To solve this, we first need to determine the translation rule from the given information. We know that the point \((2, -9)\) translates to \((4, -14)\).

### Step 1: Determine the translation vector.
The translation vector is the change in the coordinates from the original point to the new point:

- **Change in x-coordinate:** \( 4 - 2 = 2 \)
- **Change in y-coordinate:** \( -14 - (-9) = -14 + 9 = -5 \)

So, the translation vector is \((2, -5)\).

### Step 2: Apply the translation to the point \((5, 6)\).
Now, we'll apply the same translation vector \((2, -5)\) to the point \((5, 6)\):

- **New x-coordinate:** \( 5 + 2 = 7 \)
- **New y-coordinate:** \( 6 + (-5) = 6 - 5 = 1 \)

### Final Answer:
The image of the point \((5, 6)\) under the same translation is \((7, 1)\).

Would you like any further clarification or details on this?

### Related questions:
1. What is a translation in geometry?
2. How do you find the translation vector between two points?
3. What happens to a figure when it undergoes translation?
4. Can a translation change the shape or size of a figure?
5. How do different types of transformations (translation, rotation, reflection) differ?

**Tip:** When working with translations, always find the vector first by subtracting the coordinates of the original point from the translated point.

The image of the point (2,−9) under a translation is (4,−14). Find the coordinates of the image of the point (5,6) under the same translation.

This problem involves translating the point (5, 6) under the same transformation as (2, -9) to (4, -14). The solution includes determining the translation vector and applying it to find the new point. Learn how to solve coordinate translation problems with step-by-step guidance. Suitable for students in Grades 6-8.

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