In this problem, the point $B'$ represents the new position of point $B$ after the translation along the vector $\langle -3, 3 \rangle$.

Step-by-step process:

1. Identify the original coordinates of point $B$: From the graph, the point $B$ appears to be at $(3, 1)$.

2. Apply the translation vector: The vector $\langle -3, 3 \rangle$ means you move 3 units left (in the negative $x$-direction) and 3 units up (in the positive $y$-direction).

   $B'(x', y') = (x_B - 3, y_B + 3)$

   Substituting $B(3, 1)$:

   $B'(3 - 3, 1 + 3) = B'(0, 4)$

Conclusion:

The coordinates of $B'$ after the translation are $(0, 4)$.

Would you like more details or have any questions?

Here are 5 relative questions you could explore further:

1. How would point $A$ move under the same translation vector?
2. What would happen to the triangle formed by points $A$, $B$, and $C$ after the translation?
3. How can you describe the change in the entire shape due to translation?
4. How is translation different from rotation and reflection in geometry?
5. If the vector were $\langle 2, -3 \rangle$, what would be the new coordinates of point $B'$?

Tip: Translations do not change the size or shape of figures, only their position.