Plot the point \( \left(\frac{9}{2},-\frac{3}{2}\right) \) in a rectangular coordinate system.

Sure! Let's plot the point \( \left(\frac{9}{2}, -\frac{3}{2}\right) \) on a rectangular (Cartesian) coordinate system. ### Step-by-Step Guide to Plotting the Point 1. **Understand the Coordinates:** - **\( x = \frac{9}{2} = 4.5 \):** This is the horizontal distance from the origin (0,0) along the x-axis. - **\( y = -\frac{3}{2} = -1.5 \):** This is the vertical distance from the origin along the y-axis. 2. **Draw the Coordinate Axes:** - Draw two perpendicular lines intersecting at the origin (0,0). - Label the horizontal axis as the **x-axis** and the vertical axis as the **y-axis**. - Mark equal intervals on both axes for accurate plotting. 3. **Plot the Point:** - **Move along the x-axis:** From the origin, move **4.5 units to the right** because \( x = \frac{9}{2} \) is positive. - **Move along the y-axis:** From that point, move **1.5 units down** because \( y = -\frac{3}{2} \) is negative. - Mark the point where these two movements intersect. ### Visual Representation Below is a simple ASCII representation of the coordinate system with the point plotted. Note that it's a simplified illustration. ``` y | 3 | 2 | 1 | -----|------------------ x -1 | * -2 | | ``` - **Origin (0,0):** Where the x-axis and y-axis intersect. - **Point \(\left(\frac{9}{2}, -\frac{3}{2}\right)\):** Represented by the asterisk (*) at (4.5, -1.5). ### Detailed Explanation 1. **Along the X-axis:** - Starting at the origin, move **4.5 units to the right** because the x-coordinate is positive. 2. **Along the Y-axis:** - From the position at 4.5 on the x-axis, move **1.5 units downward** because the y-coordinate is negative. 3. **Marking the Point:** - The final position after these movements is the location of the point \( \left(\frac{9}{2}, -\frac{3}{2}\right) \). ### Tips for Accurate Plotting - **Use Graph Paper:** For more precision, especially with fractional coordinates, graph paper can help maintain accurate scaling. - **Label the Axes:** Clearly label the x and y axes and mark the units to avoid confusion. - **Plot Other Points:** To get a better sense of the coordinate system, plot additional points and observe their positions relative to each other. ### Conclusion By following these steps, you can accurately plot the point \( \left(\frac{9}{2}, -\frac{3}{2}\right) \) on a rectangular coordinate system. If you have access to graphing tools or software (like Desmos, GeoGebra, or even graph paper), it will make the plotting process easier and more precise.