The mid-point of the line segment AB is (4,0). If the co-ordinates of point A is (3,-2), then coordinates of point B is _______________

Answer

To find the coordinates of point B given the midpoint of line segment AB and the coordinates of point A, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Midpoint M = (4, 0)
- Coordinates of point A = (3, -2)
- Coordinates of point B = (x, y) (unknown)

2. **Use the Midpoint Formula:**
The midpoint M of a line segment connecting points A(x1, y1) and B(x2, y2) is given by the formula:
\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
Here, we can substitute the known values:
- \( x_1 = 3 \)
- \( y_1 = -2 \)
- \( M = (4, 0) \)

3. **Set Up the Equations:**
From the midpoint formula, we can set up two equations based on the x-coordinates and y-coordinates:
- For the x-coordinates:
\[ 4 = \frac{3 + x}{2} \]
- For the y-coordinates:
\[ 0 = \frac{-2 + y}{2} \]

4. **Solve for x:**
Multiply both sides of the x-coordinate equation by 2:
\[ 8 = 3 + x \]
Now, isolate x:
\[ x = 8 - 3 = 5 \]

5. **Solve for y:**
Multiply both sides of the y-coordinate equation by 2:
\[ 0 = -2 + y \]
Now, isolate y:
\[ y = 2 \]

6. **Conclusion:**
The coordinates of point B are (5, 2).

### Final Answer:
Coordinates of point B = (5, 2)

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