Find the midpoint of the line joining the points `(4, -1) and (-2, -3)`.

Answer

To find the midpoint of the line joining the points \( (4, -1) \) and \( (-2, -3) \), we can follow these steps:

### Step 1: Identify the coordinates of the points
Let point A be \( (x_1, y_1) = (4, -1) \) and point B be \( (x_2, y_2) = (-2, -3) \).

### Step 2: Use the midpoint formula
The formula for finding 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 3: Substitute the coordinates into the formula
Substituting the coordinates of points A and B into the midpoint formula:
\[ M = \left( \frac{4 + (-2)}{2}, \frac{-1 + (-3)}{2} \right) \]

### Step 4: Calculate the x-coordinate of the midpoint
Calculating the x-coordinate:
\[ \frac{4 - 2}{2} = \frac{2}{2} = 1 \]

### Step 5: Calculate the y-coordinate of the midpoint
Calculating the y-coordinate:
\[ \frac{-1 - 3}{2} = \frac{-4}{2} = -2 \]

### Step 6: Write the final result
Thus, the midpoint \( M \) of the line segment joining the points \( (4, -1) \) and \( (-2, -3) \) is:
\[ M = (1, -2) \]

### Final Answer
The midpoint is \( (1, -2) \).

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