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The problem in the image states that a line segment \( VW \) is divided by point \( U \) such that the ratio \( VU:UW \) is \( 3:1 \). Your task is to graph point \( U \) on the given line. Let's go through the solution:

1. **Identifying Coordinates of Points V and W:**
   - Point \( V \) is at approximately \( (2, 4) \).
   - Point \( W \) is at approximately \( (14, 18) \).

2. **Using the Section Formula:**
   Since \( U \) divides the line in the ratio \( 3:1 \), we apply the section formula for internal division:
   \[
   U(x, y) = \left( \frac{m \cdot x_2 + n \cdot x_1}{m+n}, \frac{m \cdot y_2 + n \cdot y_1}{m+n} \right)
   \]
   where \( (x_1, y_1) \) and \( (x_2, y_2) \) are the coordinates of points \( V \) and \( W \), and \( m:n \) is the given ratio.

   Here, \( m = 3 \) and \( n = 1 \), and the coordinates of \( V \) are \( (2, 4) \) and \( W \) are \( (14, 18) \).

3. **Calculating Coordinates of U:**
   \[
   U(x, y) = \left( \frac{3 \cdot 14 + 1 \cdot 2}{3+1}, \frac{3 \cdot 18 + 1 \cdot 4}{3+1} \right)
   \]
   Simplifying the calculations:
   \[
   U(x, y) = \left( \frac{42 + 2}{4}, \frac{54 + 4}{4} \right) = \left( \frac{44}{4}, \frac{58}{4} \right) = (11, 14.5)
   \]

Thus, point \( U \) has coordinates \( (11, 14.5) \). You can graph it at that location on the given grid.

Would you like further details or have any questions?

Here are 5 related questions:
1. How do you calculate the midpoint of a line segment?
2. Can the section formula be used if \( U \) divides the line externally?
3. What is the distance formula between two points on a plane?
4. How would the coordinates change if the ratio \( VU:UW \) were \( 2:1 \)?
5. How do you find the slope of a line given two points?

**Tip:** When dealing with line division problems, always ensure to correctly identify the ratio and whether the division is internal or external to avoid calculation errors.

VW is divided by point U such that VU:UW is 3:1. Graph U.

Learn how to graph point U on the line segment VW where the ratio VU:UW is 3:1. This problem explores key concepts in coordinate geometry, including the section formula for internal division, and is suitable for students in Grades 9-10.

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