The co - ordinates of midpoint of the points `(-3, 4)` and `(1, -2)` are :

Options

A. `(1, -2)`
B. `(-2, 3)`
C. `(2, 1)`
D. `(-2,-3)`

Answer

To find the coordinates of the midpoint of the points \((-3, 4)\) and \((1, -2)\), we can use the midpoint formula.

### Step-by-step Solution:

1. **Identify the Coordinates:**
Let the points be:
- Point A: \((x_1, y_1) = (-3, 4)\)
- Point B: \((x_2, y_2) = (1, -2)\)

2. **Apply the Midpoint Formula:**
The formula for the midpoint \(M\) of two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right) \]

3. **Calculate the x-coordinate of the Midpoint:**
Substitute the values of \(x_1\) and \(x_2\):
\[ x_M = \frac{-3 + 1}{2} = \frac{-2}{2} = -1 \]

4. **Calculate the y-coordinate of the Midpoint:**
Substitute the values of \(y_1\) and \(y_2\):
\[ y_M = \frac{4 + (-2)}{2} = \frac{4 - 2}{2} = \frac{2}{2} = 1 \]

5. **Combine the Coordinates:**
Therefore, the coordinates of the midpoint \(M\) are:
\[ M = (-1, 1) \]

### Final Answer:
The coordinates of the midpoint of the points \((-3, 4)\) and \((1, -2)\) are \((-1, 1)\).

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