The midpoint of the line segment joining the points `(-4, 3) and (8, -5)` is :

Options

A. `(-12, 8)`
B. `(4, -2)`
C. `(-2, 1)`
D. `(2, -1)`

Answer

To find the midpoint of the line segment joining the points \((-4, 3)\) and \((8, -5)\), we can use the midpoint formula. The formula for the midpoint \(M\) of a line segment joining two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:

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

### Step-by-Step Solution:

1. **Identify the coordinates of the points:**
- Let \((x_1, y_1) = (-4, 3)\)
- Let \((x_2, y_2) = (8, -5)\)

2. **Calculate the x-coordinate of the midpoint:**
\[ x_M = \frac{x_1 + x_2}{2} = \frac{-4 + 8}{2} \]
\[ x_M = \frac{4}{2} = 2 \]

3. **Calculate the y-coordinate of the midpoint:**
\[ y_M = \frac{y_1 + y_2}{2} = \frac{3 + (-5)}{2} \]
\[ y_M = \frac{3 - 5}{2} = \frac{-2}{2} = -1 \]

4. **Combine the x and y coordinates to get the midpoint:**
\[ M = (x_M, y_M) = (2, -1) \]

Thus, the midpoint of the line segment joining the points \((-4, 3)\) and \((8, -5)\) is \((2, -1)\).