To determine the coordinates of $K'$ and $M'$ after the translation, we follow these steps:

1. Identify the original coordinates of $K$ and $M$:

   • From the graph:
     • $K$ is at $(4,1)$.
     • $M$ is at $(2,-1)$.

2. Apply the translation vector $(-6,2)$:

   • Translation means shifting each point by adding the vector components: $(x', y') = (x + (-6), y + 2)$

3. Calculate new coordinates:

   • For $K'$: $K' = (4 - 6, 1 + 2) = (-2,3)$
   • For $M'$: $M' = (2 - 6, -1 + 2) = (-4,1)$

Final Answer:

a) The coordinates of $K'$ are (-2,3).
b) The coordinates of $M'$ are (-4,1).

Would you like a step-by-step explanation of the translation process?

Here are five related questions to explore further:

1. How would the shape change if translated by vector $(3,-4)$?
2. What are the new coordinates of $J'$ and $L'$ after the translation?
3. How do you determine the translation vector if given original and translated points?
4. What is the effect of a translation on the size and orientation of a shape?
5. How can translations be represented using matrix transformations?

Tip: A translation moves a shape without changing its size, shape, or orientation—just shifts it in the plane. 🚀