1 The point \(A\) has coordinates \(( 6,5 )\) and the point \(B\) has coordinates \(( 2 , - 1 )\).
- Find the coordinates of the midpoint of \(A B\).
- Show that \(A B\) has length \(k \sqrt { 13 }\), where \(k\) is an integer.
- Find the gradient of the line \(A B\).
- Hence, or otherwise, show that the line \(A B\) has equation \(3 x - 2 y = 8\).
- The line \(A B\) intersects the line with equation \(2 x + y = 10\) at the point \(C\). Find the coordinates of \(C\).