In the coordinate plane, for a triangle ABC with area 9, let P, Q, R be points moving on the three sides AB, BC, CA respectively. When
$$\overrightarrow { \mathrm { AX } } = \frac { 1 } { 4 } ( \overrightarrow { \mathrm { AP } } + \overrightarrow { \mathrm { AR } } ) + \frac { 1 } { 2 } \overrightarrow { \mathrm { AQ } }$$
is satisfied, the area of the region represented by point X is $\frac { q } { p }$. Find the value of $p + q$. (Here, $p$ and $q$ are coprime natural numbers.) [4 points]