5. The points \(A\) and \(B\) have coordinates \(( 4,6 )\) and \(( 12,2 )\) respectively.
The straight line \(l _ { 1 }\) passes through \(A\) and \(B\).
- Find an equation for \(l _ { 1 }\) in the form \(a x + b y = c\), where \(a\), b and \(c\) are integers.
The straight line \(l _ { 2 }\) passes through the origin and has gradient - 4 .
- Write down an equation for \(l _ { 2 }\).
The lines \(l _ { 1 }\) and \(l _ { 2 }\) intercept at the point \(C\).
- Find the exact coordinates of the mid-point of \(A C\).