To determine the translation, we need to find how the point $B(-5, -2)$ is shifted to become $B'(6, -5)$.

A translation moves a point by adding a fixed amount to both the $x$- and $y$-coordinates. The translation vector $(a, b)$ can be found as:

$a = x' - x$ $b = y' - y$

Where:

• $(x, y)$ is the original point $B(-5, -2)$,
• $(x', y')$ is the image point $B'(6, -5)$.

Step 1: Calculate the change in the $x$-coordinate:

$a = 6 - (-5) = 6 + 5 = 11$

Step 2: Calculate the change in the $y$-coordinate:

$b = -5 - (-2) = -5 + 2 = -3$

Thus, the translation is by the vector $(11, 3)$.

The translation that maps $B(-5, -2)$ to $B'(6, -5)$ is $(11, 3)$.

Would you like further details or clarifications?

Here are five related questions:

1. How do you express translations in terms of vector notation?
2. What is the general formula for translating any point by a vector?
3. How can translations be used in geometric transformations?
4. How do translations affect the shape and size of geometric figures?
5. How would you apply a translation to a 3D coordinate?

Tip: Always check both coordinates (x and y) separately when determining the translation vector.