Let $$ P(-2,1) $$ and $$ Q(6,8) $$ be two points in the coordinate plane. (a) Plot $$ P $$ and $$ Q $$ in the coordinate plane.

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UpStudy AI · Accepted Answer

Sure! Let's plot the points $$ P(-2, 1) $$ and $$ Q(6, 8) $$ on the coordinate plane.

### Step-by-Step Guide to Plotting the Points:

1. **Draw the Coordinate Axes:**
   - Draw a horizontal line for the **x-axis** and a vertical line for the **y-axis**. Label the point where they intersect as the **origin (0,0)**.

2. **Mark the Units:**
   - Decide on a scale (e.g., each grid square represents 1 unit).
   - Label the axes with appropriate numbers. For this example, we'll consider:
     - **x-axis:** from -4 to 8
     - **y-axis:** from 0 to 10

3. **Plot Point $$ P(-2, 1) $$:**
   - Start at the origin.
   - Move **2 units to the left** along the x-axis (since the x-coordinate is -2).
   - Move **1 unit up** along the y-axis (since the y-coordinate is 1).
   - Mark the point and label it as $$ P(-2, 1) $$.

4. **Plot Point $$ Q(6, 8) $$:**
   - Start at the origin.
   - Move **6 units to the right** along the x-axis (since the x-coordinate is 6).
   - Move **8 units up** along the y-axis (since the y-coordinate is 8).
   - Mark the point and label it as $$ Q(6, 8) $$.

### Visual Representation:

Below is an ASCII representation of the coordinate plane with the points plotted:

```
y
10 |                       
 9 |                       
 8 |                      Q(6,8)
 7 |                       
 6 |                       
 5 |                       
 4 |                       
 3 |                       
 2 |                       
 1 |      P(-2,1)          
 0 |______________________________ x
    -4  -3  -2  -1   0   1   2   3   4   5   6   7   8
```

### Explanation of the Plot:

- **Point $$ P(-2, 1) $$:**
  - Located 2 units to the left of the origin on the x-axis and 1 unit above the x-axis on the y-axis.

- **Point $$ Q(6, 8) $$:**
  - Located 6 units to the right of the origin on the x-axis and 8 units above the x-axis on the y-axis.

### Graphical Plot:

If you prefer a graphical representation, here's how the points appear on the coordinate plane:

![Coordinate Plane with Points P(-2,1) and Q(6,8)](https://i.imgur.com/YourImageLink.png)

*(Please replace the image link with an actual plot if you're creating one using graphing software or drawing tools.)*

### Summary:

- **Point P(-2, 1):** Located in the second quadrant.
- **Point Q(6, 8):** Located in the first quadrant, higher up on the plane.

By following these steps, you can accurately plot any points on the coordinate plane.
Plot the points $$ P(-2, 1) $$ and $$ Q(6, 8) $$ on the coordinate plane by moving 2 units left and 1 unit up for $$ P $$, and 6 units right and 8 units up for $$ Q $$.

Let \( P(-2,1) \) and \( Q(6,8) \) be two points in the coordinate plane. (a) Plot \( P \) and \( Q \) in the coordinate plane.

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