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The problem states:

- The coordinates of the endpoints of \( UV \) are \( U(1, -6) \) and \( V(11, 9) \).
- Point \( W \) is on \( UV \) and divides it such that the ratio \( UW : VW = 3:2 \).
  
We need to find the coordinates of \( W \).

### Solution Approach:

We can use the section formula. If a point divides a line segment in a ratio \( m:n \), the coordinates \( (x, y) \) of the dividing point are given by:

\[
x = \frac{m \cdot x_2 + n \cdot x_1}{m+n}, \quad y = \frac{m \cdot y_2 + n \cdot y_1}{m+n}
\]

Where:
- \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of the endpoints of the line.
- \( m:n \) is the given ratio.

In this case:
- \( (x_1, y_1) = (1, -6) \) and \( (x_2, y_2) = (11, 9) \),
- The ratio \( m:n = 3:2 \).

Let's now calculate the coordinates of \( W \). I'll do the math.

The coordinates of the endpoints of UV are U(1, -6) and V(11, 9). Point W is on UV and divides it such that UW:VW is 3:2. What are the coordinates of W? Write your answers as integers or decimals.

Learn how to find the coordinates of a point that divides a line segment in a 3:2 ratio using the section formula. The problem involves two endpoints U(1, -6) and V(11, 9), and the dividing point W is calculated based on given ratios. Suitable for students in Grades 8-10.

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