Reasoning about invariance under translation (4 marks)

Triangle $P$ has area $18\,\text{cm}^2$ and perimeter $20\,\text{cm}$. Triangle $P$ is translated by the column vector $\begin{pmatrix} 9 \\ -12 \end{pmatrix}$ to give triangle $P'$.

(a) Write down the area of triangle $P'$. (1) (b) Write down the perimeter of triangle $P'$. (1) (c) Explain, with reference to the properties of a translation, why your answers to (a) and (b) must be the same as for triangle $P$. (2)