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

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:  *(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.