A (-3,2) and B(5,4) are the end points of a lline segment , find the coordinates of the mid points of the line segment :

Options

A. (1,3)
B. (2,3)
C. (3,2)
D. (4,3)

Answer

To find the midpoint of the line segment with endpoints A(-3, 2) and B(5, 4), we will use the midpoint formula. The midpoint M of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:

\[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \]

### Step-by-Step Solution:

1. **Identify the coordinates of points A and B:**
- Point A has coordinates (-3, 2), so \(x1 = -3\) and \(y1 = 2\).
- Point B has coordinates (5, 4), so \(x2 = 5\) and \(y2 = 4\).

2. **Substitute the coordinates into the midpoint formula:**
\[ M = \left( \frac{-3 + 5}{2}, \frac{2 + 4}{2} \right) \]

3. **Calculate the x-coordinate of the midpoint:**
- First, calculate \(-3 + 5\):
\[ -3 + 5 = 2 \]
- Now divide by 2:
\[ \frac{2}{2} = 1 \]

4. **Calculate the y-coordinate of the midpoint:**
- First, calculate \(2 + 4\):
\[ 2 + 4 = 6 \]
- Now divide by 2:
\[ \frac{6}{2} = 3 \]

5. **Combine the results to find the midpoint:**
- The coordinates of the midpoint M are:
\[ M = (1, 3) \]

### Final Answer:
The coordinates of the midpoint of the line segment AB are (1, 3).

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