In each of the following find the value of k for which the points are collinear.
(i) `(7, –2), (5, 1), (3, k)`
(ii) `(8, 1), (k, – 4), (2, –5)`

Explanation

To find the value of \( k \) for which the points are collinear, we can use the area of the triangle formed by the three points. If the area is zero, then the points are collinear.

### Part (i): Points (7, -2), (5, 1), (3, k)

1. **Use the area 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|
...