If the points A (x,y), B (1,4) and C (-2,5) are collinear, then shown that x + 3y = 13.

Explanation

To show that the points A (x, y), B (1, 4), and C (-2, 5) are collinear and that \( x + 3y = 13 \), we can use the formula for the area of a triangle formed by three points. If the area is zero, the points are collinear.

### Step-by-Step Solution:

1. **Area of Triangle Formula**:
The area \( A \) of a triangle formed by points \( (x_1, y_1) \), \( (x_2, y_2) \), and \( (x_3, y_3) \) is given by:
\[
A = \frac{1}{2} \left| x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2) \right|
...