You really need to do three things:
1) translate the point (2,5) to (0,0)
2) rotate about (0,0) 70 degrees
3) translate (0,0) back to 2,5).
In homogeneous coordinates, the point (a, b) is represented by the array [a, b, 1] with the understanding that any multiple, [sa, sb, s], is equivalent to the point (a,b). That is, if the third component is not 1, divide the entire array by that component to get the point.
The advantage of homogenous coordinates (they are used a lot in computer graphics) is that you can represent translation as a matrix multiplication. For example:
\begin{bmatrix}1 & 0 & a \\ 0 & 1 & b\\ 0 & 0 & 1\end{bmatrix}\begin{bmatrix}x \\ y \\ 1\end{bmatrix}= \begin{bmatrix}x+ a \\ y+ b \\ 1\end{bmatrix}.
Of course, rotation around the origin, by \theta degrees, is given by
\begin{bmatrix}cos(\theta) & -sin(\theta) & 1 \\ sin(\theta) & cos(\theta) & 0 \\ 0 & 0 & 1\end{bmatrix}.
To solve this problem you need to construct three matrices: the matrix, A, that translates (2, 5) to (0, 0), the matrix, B, that rotates 70 degrees around (0,0), and the matrix, C, that translates (0, 0) to (2, 5) (It will, of course, be the inverse of the matrix A). Finally multiply the matrices in order CBA.
The point (8, 7) is represented by the array [8, 7, 1].