https://file.aiquickdraw.com/mathbot/file/1728997542315n7yy3kwm.jpg

To solve this problem, we need to translate each of the vertices of the quadrilateral 8 units left and 7 units down. Let's break this down step-by-step.

### Step 1: Translation Rules
- **8 units left** means subtract 8 from the x-coordinate.
- **7 units down** means subtract 7 from the y-coordinate.

### Step 2: Initial Coordinates
From the graph, we can identify the coordinates of the vertices:
- \( S(0, 8) \)
- \( R(6, 8) \)
- \( Q(6, -2) \)
- \( P(0, -2) \)

### Step 3: Applying the Translation
- **For point \( S(0, 8) \)**:
  - New x-coordinate: \( 0 - 8 = -8 \)
  - New y-coordinate: \( 8 - 7 = 1 \)
  - New position of \( S' \): \( (-8, 1) \)

- **For point \( R(6, 8) \)**:
  - New x-coordinate: \( 6 - 8 = -2 \)
  - New y-coordinate: \( 8 - 7 = 1 \)
  - New position of \( R' \): \( (-2, 1) \)

- **For point \( Q(6, -2) \)**:
  - New x-coordinate: \( 6 - 8 = -2 \)
  - New y-coordinate: \( -2 - 7 = -9 \)
  - New position of \( Q' \): \( (-2, -9) \)

- **For point \( P(0, -2) \)**:
  - New x-coordinate: \( 0 - 8 = -8 \)
  - New y-coordinate: \( -2 - 7 = -9 \)
  - New position of \( P' \): \( (-8, -9) \)

### Step 4: Final Coordinates After Translation
The new coordinates of the vertices are:
- \( S'(-8, 1) \)
- \( R'(-2, 1) \)
- \( Q'(-2, -9) \)
- \( P'(-8, -9) \)

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Do you have any questions or would you like further details on any step?

Here are 5 related questions to deepen your understanding:
1. How do you determine the direction and distance of a translation on a coordinate plane?
2. How would the coordinates change if the translation was 5 units right and 3 units up?
3. What happens to the shape of the figure after translation? Does it change?
4. Can you describe how reflection differs from translation on the coordinate plane?
5. What would the new coordinates be if you translated the figure 10 units left and 5 units up instead?

**Tip:** When performing a translation, remember to apply the same transformation rule (e.g., subtract or add) to all points' x- and y-coordinates consistently!

Write the coordinates of the vertices after a translation 8 units left and 7 units down.

Learn how to translate a quadrilateral by 8 units left and 7 units down on a coordinate plane. Identify the new coordinates of the vertices after translation. This problem covers the key concept of translation in coordinate geometry. Suitable for students in Grades 6-8.

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