We are given the coordinates of a triangle and are asked for the coordinates of a new point after translating it 2 units to the right and 1 unit up. Therefore, the changes in the coordinates are as follows, we add 2 units to the x coordinates and 1 to the y coordinates:
![\begin{gathered} A^(\prime)=(4+2,2+1)=(6,3) \\ B^(\prime)=(2+2,7+1)=(4,8) \\ C^(\prime)=(10+2,5+1)=(12,6) \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/unrjp58w09y1hyt8e59ywtmizn8p8ldo4a.png)
Therefore, the location of final point B´ is (4,8)