https://file.aiquickdraw.com/mathbot/file/1726786359115dvsoox9p.jpg

To solve the problem in the image, we need to translate the vertices \( K \), \( L \), \( M \), and \( N \) 3 units to the right and 8 units down. Translation involves adjusting the coordinates accordingly.

### Step 1: Original Coordinates of the Vertices
From the image, we can identify the coordinates of the vertices:
- \( K(1, 2) \)
- \( L(1, 10) \)
- \( M(7, 10) \)
- \( N(7, 2) \)

### Step 2: Translation Rule
Translation by 3 units to the right increases the x-coordinate by 3.
Translation by 8 units down decreases the y-coordinate by 8.

### Step 3: Apply the Translation
Let’s now apply the translation rule to each vertex:

1. \( K(1, 2) \) → \( K'(1 + 3, 2 - 8) = K'(4, -6) \)
2. \( L(1, 10) \) → \( L'(1 + 3, 10 - 8) = L'(4, 2) \)
3. \( M(7, 10) \) → \( M'(7 + 3, 10 - 8) = M'(10, 2) \)
4. \( N(7, 2) \) → \( N'(7 + 3, 2 - 8) = N'(10, -6) \)

### Step 4: Final Translated Coordinates
- \( K'(4, -6) \)
- \( L'(4, 2) \)
- \( M'(10, 2) \)
- \( N'(10, -6) \)

These are the coordinates of the vertices after the given translation.

Do you need more details or have any questions?

Here are some related questions for further practice:
1. What would happen to the coordinates if the translation was 5 units left and 4 units up?
2. Can you describe the rule for a reflection over the y-axis and apply it to these points?
3. What is the area of the rectangle formed by the original vertices?
4. How would you describe a dilation transformation for these points with a factor of 2?
5. Can you calculate the perimeter of the shape after translation?

**Tip:** Always break down each transformation step-by-step to avoid confusion!

Write the coordinates of the vertices after a translation 3 units right and 8 units down.

Learn how to translate the vertices of a rectangle by 3 units to the right and 8 units down. Follow the step-by-step process to adjust the coordinates, including examples. This concept applies to Grades 6-8 and focuses on coordinate geometry.

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