The point P(x, y) is first reflected in the x-axis and then reflected in the origin to P'. If P' has co-ordinates (-8, 5), evaluate x and y.

Answer

To solve the problem, we will follow the steps of reflecting the point \( P(x, y) \) first in the x-axis and then in the origin to find the coordinates of \( P' \) and evaluate \( x \) and \( y \).

### Step-by-Step Solution:

1. **Reflect Point P in the x-axis**:
- The reflection of a point \( P(x, y) \) in the x-axis results in the point \( P_1(x, -y) \).
- This means the y-coordinate changes sign while the x-coordinate remains the same.

2. **Reflect Point P_1 in the Origin**:
- The reflection of a point \( P_1(x, -y) \) in the origin results in the point \( P'(-x, y) \).
- Here, both the x and y coordinates change their signs.

3. **Given Coordinates of P'**:
- We are given that \( P' \) has coordinates \( (-8, 5) \).
- Therefore, we can set up the equations based on the reflection process:
\[ -x = -8 \quad \text{(1)} \]
\[ y = 5 \quad \text{(2)} \]

4. **Solve for x**:
- From equation (1):
\[ -x = -8 \implies x = 8 \]

5. **Solve for y**:
- From equation (2):
\[ y = 5 \]

6. **Final Values**:
- Thus, the values of \( x \) and \( y \) are:
\[ x = 8, \quad y = 5 \]

### Summary:
The coordinates of point \( P \) are \( (8, 5) \).