https://file.aiquickdraw.com/mathbot/file/17296299363009vdl7h75.jpg

To find the coordinates of \( K' \) and \( M' \), we need to apply the translation vector \( \left( -6, 2 \right) \) to the original coordinates of points \( K \) and \( M \).

### Step 1: Identify the original coordinates
From the graph:
- Point \( K \) is located at \( (4, 1) \).
- Point \( M \) is located at \( (1, -5) \).

### Step 2: Apply the translation vector
The translation vector is \( \left( -6, 2 \right) \), which means we subtract 6 from the \( x \)-coordinate and add 2 to the \( y \)-coordinate.

#### a) Finding the coordinates of \( K' \):
- Original coordinates of \( K \): \( (4, 1) \).
- Applying the translation: 
  \[
  K' = (4 - 6, 1 + 2) = (-2, 3).
  \]

#### b) Finding the coordinates of \( M' \):
- Original coordinates of \( M \): \( (1, -5) \).
- Applying the translation:
  \[
  M' = (1 - 6, -5 + 2) = (-5, -3).
  \]

### Final Answers:
- The coordinates of \( K' \) are \( (-2, 3) \).
- The coordinates of \( M' \) are \( (-5, -3) \).

Would you like further details or have any questions?

### Related Questions:
1. What would be the new coordinates if the translation vector were \( (3, -4) \)?
2. How would the shape of the figure change if the vector had a magnitude of \( \sqrt{45} \) in a different direction?
3. How can we determine the translation vector given the original and translated coordinates of any two points?
4. What is the effect of translating a shape by a vector with both positive components?
5. How do we find the midpoint of a line segment before and after translation?

### Tip:
Always double-check the direction of translation by noting if the vector components are positive or negative, which indicates movement along the respective axes.

J'K'L'M' is a translation of JKLM by vector (-6, 2). a) What are the coordinates of K'? b) What are the coordinates of M'?

Learn how to solve a translation problem by applying a vector (-6, 2) to the shape JKLM. This problem uses coordinate geometry to find the new coordinates of points K' and M'. Suitable for students in Grades 6-8.

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