Connor Cofield - Open Middle task is से © Slideshow Background Layout Theme | Transition OPEN MIDDLE - Graphing Points on a Coordinate Plane Make four points using the integers -4 to 4 at most one time each so that each point is in a different quadrant. Tegs 6 NS 8 DOK 2. SKILL $$ / $$ CONCEPT ROBERT KAPLINSKY $$ ( $$ , ___ ) (_ ) ( ) , _ ) -4 -3 $$ -2 $$ -1 0 1 2 3 4

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UpStudy AI · Accepted Answer

Certainly! Let's break down the **Open Middle Task** you've provided and work through it step by step.

### **Task Overview**
**Objective:**  
Create four points on a coordinate plane using the integers from **-4 to 4** (each integer used **at most once**) such that each point resides in a **different quadrant**.

### **Understanding the Quadrants**
The coordinate plane is divided into four quadrants:

1. **Quadrant I**: (+, +)  
2. **Quadrant II**: (-, +)  
3. **Quadrant III**: (-, -)  
4. **Quadrant IV**: (+, -)

**Note:**  
- **Zero (0)** is not included in any quadrant. Since we're using integers from -4 to 4 **excluding 0**, we don't have to worry about points lying on the axes.

### **Step-by-Step Solution**

1. **List the Available Integers:**  
   - Negative: -4, -3, -2, -1  
   - Positive: 1, 2, 3, 4

2. **Assign Integers to Each Quadrant:**  
   Since each integer can be used **only once**, we'll carefully assign them to ensure no repeats.

- **Quadrant I (+, +):** Both coordinates are positive.  
     - Let's choose **(1, 2)**  
     - *Uses integers: 1 and 2*

- **Quadrant II (-, +):** X is negative, Y is positive.  
     - Let's choose **(-3, 4)**  
     - *Uses integers: -3 and 4*

- **Quadrant III (-, -):** Both coordinates are negative.  
     - Let's choose **(-4, -1)**  
     - *Uses integers: -4 and -1*

- **Quadrant IV (+, -):** X is positive, Y is negative.  
     - Let's choose **(3, -2)**  
     - *Uses integers: 3 and -2*

3. **Final Points:**
   - **Quadrant I:** $$(1, 2)$$
   - **Quadrant II:** $$(-3, 4)$$
   - **Quadrant III:** $$(-4, -1)$$
   - **Quadrant IV:** $$(3, -2)$$

4. **Verification:**  
   Ensure no integer is used more than once:
   - **Used Integers:** 1, 2, -3, 4, -4, -1, 3, -2  
   - **All unique:** ✔️

### **Visual Representation**

To help you visualize, here's how the points would appear on the coordinate plane:

```
Quadrant II (-3, 4)        Quadrant I (1, 2)

Quadrant III (-4, -1)      Quadrant IV (3, -2)
```

### **Alternative Solutions**

There are multiple ways to assign the integers while meeting the criteria. Here's another valid set of points:

- **Quadrant I:** $$(2, 3)$$
- **Quadrant II:** $$(-1, 4)$$
- **Quadrant III:** $$(-4, -2)$$
- **Quadrant IV:** $$(3, -1)$$

**Note:** Always ensure that each integer from -4 to 4 is used **only once** and that each point is placed in a **different quadrant**.

### **Tips for Similar Problems**

- **Start with Unique Assignments:** Assign unique integers to each quadrant first before pairing them.
- **Avoid Repetition:** Keep track of which integers you've already used to prevent duplication.
- **Check Quadrant Rules:** Ensure that the signs of your coordinates match the requirements of their respective quadrants.

Feel free to try creating your own set of points using this method! If you have any further questions or need additional assistance, I'm here to help.
To complete the Open Middle task, assign each integer from -4 to 4 to a unique point in each quadrant: - **Quadrant I (+, +):** (1, 2) - **Quadrant II (-, +):** (-3, 4) - **Quadrant III (-, -):** (-4, -1) - **Quadrant IV (+, -):** (3, -2) These points use each integer once and are placed in different quadrants.

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