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This is a statics problem where we are tasked with determining the unknown loads \( P \) and \( Q \) acting on the foundation plate. The foundation is subjected to forces from four columns, and we know that the resultant force passes through the point \((6, 8)\).

### Problem Breakdown:
- The forces applied at the four corners of the plate are:
  - \( P \) at point \( A \) (4 m, 6 m).
  - \( 50 \, \text{kN} \) at point \( B \) (6 m, 0 m).
  - \( Q \) at point \( D \) (0 m, 5 m).
  - \( 15 \, \text{kN} \) at point \( C \) (5 m, 5 m).
  
- The resultant force is located at the coordinates \((x_r, y_r) = (6, 8)\).

To solve for \( P \) and \( Q \), we will use the following steps:
1. **Equilibrium of Forces**: The sum of all vertical forces should equal the total resultant force.
   
2. **Moment Equilibrium**: The moment generated by each force about a reference point (usually the origin) should equal the moment generated by the resultant force at the known location \((6, 8)\).

### Step-by-Step Approach:

1. **Force Equilibrium**:
   \[
   \sum F_z = P + 50 + Q + 15 = R_z
   \]
   where \( R_z \) is the resultant force in the z-direction.

2. **

La figura muestra una placa de cimentación sobre la cual actúan las cargas de las cuatro columnas mostradas. Determine los valores de las cargas P y Q si se sabe que la fuerza resultante pasa por el punto (x, y) = (6, 8).

In this statics problem, learn how to solve for the unknown loads P and Q acting on a foundation plate, given that the resultant force passes through (x,y) = (6,8). The problem covers equilibrium of forces and moments, using key formulas from statics.

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