Let's solve the problem step-by-step.

Problem Analysis:

• Point A (6, -2) is translated to point B (3, -7).
• The same translation is applied to point E (12, -3), and we are required to find the coordinates of point K.

Step 1: Determine the translation vector

The translation vector can be found by subtracting the coordinates of A from B:

$\vec{v} = B - A = (3 - 6, -7 - (-2)) = (-3, -5)$

So, the translation vector is $(-3, -5)$.

Step 2: Apply the translation to point E

Now, apply the same translation vector $(-3, -5)$ to point E (12, -3):

$K = E + \vec{v} = (12 + (-3), -3 + (-5)) = (12 - 3, -3 - 5) = (9, -8)$

Thus, the coordinates of point K are $(9, -8)$.

Would you like a more detailed explanation, or do you have any other questions?

Related Questions:

1. How do you find the distance between two points after a translation?
2. What is the general form of a translation vector in 2D?
3. How do you find the midpoint between two points after translation?
4. Can translations be combined with other geometric transformations (e.g., rotations)?
5. How can we describe translations using matrices?

Tip: Translations preserve the shape and size of geometric figures.