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The problem asks to find the coordinates of point \( V \) given that the midpoint \( M \) of line segment \( UV \) is at \( M(7, 4) \), and point \( U \) is located at \( U(10, 1) \).

### Midpoint Formula:
The midpoint \( M \) of a line segment connecting two points \( U(x_1, y_1) \) and \( V(x_2, y_2) \) is given by the formula:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

### Given:
- \( M(7, 4) \)
- \( U(10, 1) \)

### Step 1: Set up the system of equations
Using the midpoint formula:
\[
\frac{10 + x_2}{2} = 7
\]
\[
\frac{1 + y_2}{2} = 4
\]

### Step 2: Solve for \( x_2 \) and \( y_2 \)

1. Solve for \( x_2 \):
\[
\frac{10 + x_2}{2} = 7
\]
Multiply both sides by 2:
\[
10 + x_2 = 14
\]
\[
x_2 = 14 - 10 = 4
\]

2. Solve for \( y_2 \):
\[
\frac{1 + y_2}{2} = 4
\]
Multiply both sides by 2:
\[
1 + y_2 = 8
\]
\[
y_2 = 8 - 1 = 7
\]

### Final Answer:
The coordinates of point \( V \) are \( V(4, 7) \).

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Would you like more details or have any questions?

Here are 5 related questions to deepen your understanding:
1. How do you find the midpoint between any two given points?
2. Can the midpoint formula be used in three-dimensional space?
3. What happens if both points \( U \) and \( V \) are the same?
4. How would you verify the result for \( V(4, 7) \) by recalculating the midpoint?
5. What is the geometric significance of the midpoint on a coordinate plane?

**Tip:** Always double-check midpoint calculations by working backwards to ensure consistency.

The midpoint M of UV has coordinates (7, 4). Point U has coordinates (10, 1). Find the coordinates of point V. Write the coordinates as decimals or integers.

This problem involves finding the coordinates of point V given the midpoint M(7, 4) and point U(10, 1). Using the midpoint formula, the solution walks through calculating the coordinates of point V, making it ideal for students in Grades 7-9.

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