To find the vector that translates point $A$ to $A'$, we need to determine the difference in coordinates between these two points.

1. From the graph:

   • The coordinates of point $A$ are $(-1, 6)$.
   • The coordinates of point $A'$ are $(5, 9)$.

2. The translation vector is the difference between the coordinates of $A'$ and $A$: $\text{Vector} = A' - A = (5 - (-1), 9 - 6) = (6, 3).$

Thus, the vector that translates point $A$ to point $A'$ is $\mathbf{v} = (6, 3)$.

Would you like further details or have any questions?

Here are 5 related questions for practice:

1. What vector translates point $B$ onto point $B'$?
2. What vector translates point $C$ onto point $C'$?
3. How would the translation affect the coordinates of any arbitrary point $P(x, y)$?
4. Can you write the transformation matrix for this translation?
5. What is the general formula for finding a translation vector?

Tip: When dealing with translations, always subtract the coordinates of the original point from the coordinates of the new point to find the vector.