Point 
\[B'(6,-5)\] is the image of 
\[B(-5,-2)\] under a translation. Determine the translation.
Use non-negative numbers.

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.

Point \[B'(6,-5)\] is the image of \[B(-5,-2)\] under a translation. Determine the translation. Use non-negative numbers.

Learn how to calculate the translation vector that maps the point B(-5, -2) to B'(6, -5). This step-by-step guide explains how to find the translation in the Cartesian plane using key geometric concepts and formulas. Ideal for students in Grades 6-8.

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