https://file.aiquickdraw.com/mathbot/file/1726581019328kbune6bs.jpg

Let's break down the problem step-by-step:

### 1. Initial Coordinates of the Quadrilateral
The vertices of the quadrilateral are:
- \( P(-1, -1) \)
- \( Q(0, 4) \)
- \( R(3, 1) \)
- \( S(1, -2) \)

### 2. Translation Rule
You are asked to translate the quadrilateral 3 units to the left and 2 units up. Mathematically, this means:
- Subtract 3 from the x-coordinates.
- Add 2 to the y-coordinates.

### 3. Applying the Translation
Let's calculate the new coordinates after translation:
- For \( P(-1, -1) \):
  - New x-coordinate: \( -1 - 3 = -4 \)
  - New y-coordinate: \( -1 + 2 = 1 \)
  - New position: \( P'(-4, 1) \)
  
- For \( Q(0, 4) \):
  - New x-coordinate: \( 0 - 3 = -3 \)
  - New y-coordinate: \( 4 + 2 = 6 \)
  - New position: \( Q'(-3, 6) \)

- For \( R(3, 1) \):
  - New x-coordinate: \( 3 - 3 = 0 \)
  - New y-coordinate: \( 1 + 2 = 3 \)
  - New position: \( R'(0, 3) \)

- For \( S(1, -2) \):
  - New x-coordinate: \( 1 - 3 = -2 \)
  - New y-coordinate: \( -2 + 2 = 0 \)
  - New position: \( S'(-2, 0) \)

### 4. Resulting Coordinates
The new coordinates of the quadrilateral after translation are:
- \( P'(-4, 1) \)
- \( Q'(-3, 6) \)
- \( R'(0, 3) \)
- \( S'(-2, 0) \)

You can now plot these points on the graph for both the original and translated quadrilateral. Let me know if you'd like further assistance in drawing it!

### Follow-Up Questions:
1. What are the general rules for translating shapes on the coordinate plane?
2. How would you apply a reflection instead of a translation to the quadrilateral?
3. How would the process change if you translated 3 units right and 2 units down instead?
4. What is the relationship between the original quadrilateral and its image after translation?
5. How can you calculate the distance between corresponding points before and after the translation?

**Tip:** When translating any figure on the coordinate plane, remember that the shape, size, and orientation remain unchanged; only the position shifts.

The vertices of a quadrilateral are P(-1, -1), Q(0, 4), R(3, 1), and S(1, -2). Draw the figure and its image after a translation 3 units left and 2 units up.

Learn how to translate a quadrilateral with vertices P(-1, -1), Q(0, 4), R(3, 1), and S(1, -2) 3 units left and 2 units up on the coordinate plane. This problem demonstrates key concepts of coordinate geometry and translation. Suitable for students in Grades 6-8.

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