Using determinants show that the following points are collinear: (i) (5, 5),  (-5, 1) and (10, 7)   (ii) (1, -1),  (2, 1) and (4, 5)

Explanation

To show that the given points are collinear using determinants, we will use the determinant condition for collinearity. The points \((x_1, y_1)\), \((x_2, y_2)\), and \((x_3, y_3)\) are collinear if the following determinant is equal to zero:

\[
\begin{vmatrix}
x_1 & y_1 & 1 \\
x_2 & y_2 & 1 \\
x_3 & y_3 & 1
\end{vmatrix} = 0
...