Find the midpoint of the line joining the points (7,1) and (3,5).

Answer

To find the midpoint of the line segment joining the points (7, 1) and (3, 5), we can use the midpoint formula. The midpoint \( M \) of a line segment joining two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) is given by:

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

### Step 1: Identify the coordinates of the points
Let the points be:
- Point A: \( (x_1, y_1) = (7, 1) \)
- Point B: \( (x_2, y_2) = (3, 5) \)

### Step 2: Substitute the coordinates into the midpoint formula
Now we substitute the coordinates into the midpoint formula:

\[ M = \left( \frac{7 + 3}{2}, \frac{1 + 5}{2} \right) \]

### Step 3: Calculate the x-coordinate of the midpoint
Calculate the x-coordinate:

\[ \frac{7 + 3}{2} = \frac{10}{2} = 5 \]

### Step 4: Calculate the y-coordinate of the midpoint
Now calculate the y-coordinate:

\[ \frac{1 + 5}{2} = \frac{6}{2} = 3 \]

### Step 5: Write the final answer
Thus, the midpoint \( M \) is:

\[ M = (5, 3) \]

### Final Answer:
The midpoint of the line joining the points (7, 1) and (3, 5) is \( (5, 3) \).

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