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

Options

A. (2,5)
B. 3
C. `(13)/(2)`
D. `-(13)/(2)`

Answer

To find the coordinates of point A given that the midpoint P(0, 4) of line segment AB and the coordinates of point B are (-2, 3), we can use the midpoint formula.

### Step-by-Step Solution:

1. **Understanding the Midpoint Formula:**
The midpoint P of a line segment AB with endpoints A(x1, y1) and B(x2, y2) is given by:
\[ P\left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right) \]
Here, we know:
- Midpoint P = (0, 4)
- Coordinates of B = (-2, 3)

2. **Setting Up the Equations:**
From the midpoint formula, we can set up the following equations:
\[ \frac{x1 + (-2)}{2} = 0 \quad \text{(1)} \]
\[ \frac{y1 + 3}{2} = 4 \quad \text{(2)} \]

3. **Solving for x1:**
From equation (1):
\[ \frac{x1 - 2}{2} = 0 \]
Multiply both sides by 2:
\[ x1 - 2 = 0 \]
Adding 2 to both sides gives:
\[ x1 = 2 \]

4. **Solving for y1:**
From equation (2):
\[ \frac{y1 + 3}{2} = 4 \]
Multiply both sides by 2:
\[ y1 + 3 = 8 \]
Subtracting 3 from both sides gives:
\[ y1 = 5 \]

5. **Final Coordinates of A:**
Therefore, the coordinates of point A are:
\[ A(2, 5) \]

### Final Answer:
The coordinates of A are (2, 5).