9. The line \(L _ { 1 }\) has equation \(4 y + 3 = 2 x\)
The point \(A ( p , 4 )\) lies on \(L _ { 1 }\)
- Find the value of the constant \(p\).
The line \(L _ { 2 }\) passes through the point \(C ( 2,4 )\) and is perpendicular to \(L _ { 1 }\)
- Find an equation for \(L _ { 2 }\) giving your answer in the form \(a x + b y + c = 0\), where \(a , b\) and \(c\) are integers.
The line \(L _ { 1 }\) and the line \(L _ { 2 }\) intersect at the point \(D\).
- Find the coordinates of the point \(D\).
- Show that the length of \(C D\) is \(\frac { 3 } { 2 } \sqrt { } 5\)
A point \(B\) lies on \(L _ { 1 }\) and the length of \(A B = \sqrt { } ( 80 )\)
The point \(E\) lies on \(L _ { 2 }\) such that the length of the line \(C D E = 3\) times the length of \(C D\). - Find the area of the quadrilateral \(A C B E\).