10. The straight line \(l _ { 1 }\) has equation \(2 x + y - 14 = 0\) and crosses the \(x\)-axis at the point \(A\).
- Find the coordinates of \(A\).
The straight line \(l _ { 2 }\) is parallel to \(l _ { 1 }\) and passes through the point \(B ( - 6,6 )\).
- Find an equation for \(l _ { 2 }\) in the form \(y = m x + c\).
The line \(l _ { 2 }\) crosses the \(x\)-axis at the point \(C\).
- Find the coordinates of \(C\).
The point \(D\) lies on \(l _ { 1 }\) and is such that \(C D\) is perpendicular to \(l _ { 1 }\).
- Show that \(D\) has coordinates \(( 5,4 )\).
- Find the area of triangle \(A C D\).