The problem in the image asks for the translation of point $B(2, -1)$ by a vector $(3, 2)$.

Translation Formula:

The translation of a point $(x, y)$ by a vector $(a, b)$ is given by: $(x', y') = (x + a, y + b)$ where $(x', y')$ is the new point after translation.

Applying the Formula:

For $B(2, -1)$ and the translation vector $(3, 2)$: $x' = 2 + 3 = 5$ $y' = -1 + 2 = 1$ Thus, the new point after translation is $B'(5, 1)$.

Final Answer:

The translated point is $B'(5, 1)$.

Would you like further details on translation or have any questions?

Here are 5 related questions for practice:

1. What is the translation of the point $(4, 3)$ by the vector $(-2, 5)$?
2. How would you translate point $(-1, -4)$ by the vector $(6, 2)$?
3. What is the geometric meaning of a translation?
4. If a point is translated by vector $(a, b)$, what happens when we translate it back by $(-a, -b)$?
5. How does translation affect the slope between two points?

Tip: When translating points, always add the translation vector components directly to the coordinates of the original point.