(i) Find the equation of line joining (1,2) and (3,4) using determinants,
(ii) Find the equation of the line joining (3,1) and (9,3) using determinants.

Explanation

To find the equations of the lines joining the given points using determinants, we will follow a systematic approach. Let's solve each part step by step.

### Part (i): Find the equation of the line joining (1, 2) and (3, 4)

1. **Set up the determinant**:
We will use the determinant formula for the area of the triangle formed by three points. The points are (1, 2), (3, 4), and (x, y) where (x, y) is any point on the line. The determinant should equal zero for the points to be collinear.

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