If the points `(a_1, b_1),\ \ (a_2, b_2)` and `(a_1+a_2,\ b_1+b_2)` are collinear, show that `a_1b_2=a_2b_1` .

Explanation

To show that the points \((a_1, b_1)\), \((a_2, b_2)\), and \((a_1 + a_2, b_1 + b_2)\) are collinear, we can use the concept of the area of a triangle formed by three points in the coordinate plane. If the area of the triangle is zero, then the points are collinear.

### Step-by-Step Solution:

1. **Set Up the Determinant**:
The area of the triangle formed by the points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) can be expressed using the determinant:
\[
\text{Area} = \frac{1}{2} \left| \begin{vmatrix}
...