ABCD is a parallelogram where `A(x, y), B(5, 8), C(4, 7) and D(2, -4)`. Find :
  co-ordinates of A

Answer

To find the coordinates of point A in the parallelogram ABCD, we can use the property that the diagonals of a parallelogram bisect each other. This means that the midpoint of diagonal AC is the same as the midpoint of diagonal BD.

### Step-by-Step Solution:

1. **Identify the Coordinates**:
- Let the coordinates of A be \( A(x, y) \).
- The coordinates of B are \( B(5, 8) \).
- The coordinates of C are \( C(4, 7) \).
- The coordinates of D are \( D(2, -4) \).

2. **Find the Midpoint of Diagonal BD**:
- The midpoint \( O \) of line segment BD can be calculated using the midpoint formula:
\[ O = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \]
- Here, \( B(5, 8) \) and \( D(2, -4) \).
- Calculate:
\[ O_x = \frac{5 + 2}{2} = \frac{7}{2}, \quad O_y = \frac{8 + (-4)}{2} = \frac{4}{2} = 2 \]
- Therefore, the coordinates of midpoint \( O \) are \( O\left(\frac{7}{2}, 2\right) \).

3. **Set Up the Midpoint of AC**:
- Since \( O \) is also the midpoint of AC, we can set up the equation:
\[ O_x = \frac{x + 4}{2}, \quad O_y = \frac{y + 7}{2} \]
- Substitute \( O_x \) and \( O_y \):
\[ \frac{7}{2} = \frac{x + 4}{2} \quad (1) \]
\[ 2 = \frac{y + 7}{2} \quad (2) \]

4. **Solve for x**:
- From equation (1):
\[ 7 = x + 4 \implies x = 7 - 4 = 3 \]

5. **Solve for y**:
- From equation (2):
\[ 4 = y + 7 \implies y = 4 - 7 = -3 \]

6. **Final Coordinates of A**:
- Thus, the coordinates of point A are \( A(3, -3) \).

### Final Answer:
The coordinates of point A are \( (3, -3) \).