1. $P=(\begin{matrix}p & 2p\\-1 & 3p\end{matrix})$

where$p$ is a positive constant.

The matrix $P$ represents a linear transformation $U$.

The triangle $T$ has vertices at the points with coordinates (1, 2), (3, 2) and (2, 5).

The area of the image of $T$ under the linear transformation $U$ is 15

(a) Determine the value of$p$.