Given the preimage coordinate (9, 6), what is the coordinate's x-value of the image after a translation 6 units right and 5 units down?

To solve this translation problem:

1. **Initial coordinate**: The preimage coordinate is given as \((9, 6)\).
2. **Translation**:
   - Moving 6 units to the right: Add 6 to the x-coordinate.
   - Moving 5 units down: Subtract 5 from the y-coordinate.

**Step-by-step solution**:

- \( x \text{-value} = 9 + 6 = 15 \)
- \( y \text{-value} = 6 - 5 = 1 \)

Therefore, after the translation, the new coordinate (image) is \((15, 1)\).

The **x-value** of the image is \( \boxed{15} \).

Do you need more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. What would be the y-value of the image after this translation?
2. How do you perform a translation if you are given a vector?
3. If the original coordinate was \((9, 6)\) and the translation was 3 units left and 4 units up, what would the new coordinates be?
4. What is the general formula for translating a point \((x, y)\) by \((a, b)\)?
5. What would happen if you translated the point \((9, 6)\) by \((0, 0)\)?

**Tip**: When translating points on a coordinate plane, moving "right" increases the x-value and moving "left" decreases it, while moving "up" increases the y-value and moving "down" decreases it.

Solve a translation problem where a point at (9, 6) is moved 6 units right and 5 units down. This covers basic concepts of coordinate geometry and point translation, suitable for Grades 6-8 students. Learn how to apply translation formulas to find the new coordinates.

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