and be two points in the coordinate plane.
a) Plot and in the coordinate plane.

Step-by-Step Guide to Plotting Points

1. Draw the Coordinate Axes:
   • Draw a horizontal line for the x-axis and a vertical line for the y-axis. Label the intersection as the origin (0, 0).
   • Decide on an appropriate scale for both axes (e.g., each unit represents 1 unit in the plane).
2. Plot Point :
   • X-coordinate (-2): Since it’s negative, move 2 units to the left of the origin along the x-axis.
   • Y-coordinate (1): From that position, move 1 unit up along the y-axis.
   • Mark the Point: Place a dot at this location and label it as .
3. Plot Point :
   • X-coordinate (6): Move 6 units to the right of the origin along the x-axis.
   • Y-coordinate (8): From that position, move 8 units up along the y-axis.
   • Mark the Point: Place a dot at this location and label it as .

Visual Representation

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

Using LaTeX with TikZ for a Precise Plot

\documentclass{standalone}
\usepackage{tikz}

\begin{document}

\begin{tikzpicture}[scale=0.5]
    % Draw axes
    \draw[->] (-5,0) -- (8,0) node[right] {$x$};
    \draw[->] (0,-1) -- (0,10) node[above] {$y$};
    
    % Draw grid
    \draw[step=1cm,gray,very thin] (-5,-1) grid (8,10);
    
    % Plot point P(-2,1)
    \filldraw[red] (-2,1) circle (5pt) node[below left] {$P(-2,1)$};
    
    % Plot point Q(6,8)
    \filldraw[blue] (6,8) circle (5pt) node[above right] {$Q(6,8)$};
    
    % Optional: dashed lines to axes
    \draw[dashed] (-2,0) -- (-2,1);
    \draw[dashed] (0,1) -- (-2,1);
    
    \draw[dashed] (6,0) -- (6,8);
    \draw[dashed] (0,8) -- (6,8);
\end{tikzpicture}

\end{document}

• Axes: The \draw[->] commands draw the x and y axes with arrows.
• Grid: The \draw[step=1cm,gray,very thin] command creates a light grid to help visualize the points’ locations.
• Points:
  • Point is plotted in red and labeled accordingly.
  • Point is plotted in blue and labeled accordingly.
• Dashed Lines: These help in visualizing the projection of each point onto the axes.

Final Plot