To plot the point [tex]\((5, -1)\)[/tex] in a rectangular coordinate system, we follow these steps:
1. Understand the Rectangular Coordinate System:
- The rectangular coordinate system consists of two perpendicular axes: the horizontal axis (x-axis) and the vertical axis (y-axis).
- The point where the axes intersect is called the origin, marked as (0, 0).
2. Identify the Coordinates:
- The point given is [tex]\((5, -1)\)[/tex].
- The first number, 5, is the x-coordinate, which indicates the horizontal distance from the origin.
- The second number, -1, is the y-coordinate, which indicates the vertical distance from the origin.
3. Mark the x-coordinate:
- From the origin, move 5 units to the right along the x-axis because the x-coordinate is positive.
4. Mark the y-coordinate:
- From the position at [tex]\(x = 5\)[/tex], move 1 unit down along the y-axis because the y-coordinate is negative.
5. Plotting the Point:
- After moving 5 units to the right and 1 unit down, mark the point. This is the location of the point [tex]\((5, -1)\)[/tex].
6. Illustrate the Plot:
- Draw the axes with appropriate scale.
- Label the x-axis and y-axis.
- Plot and label the point [tex]\((5, -1)\)[/tex].
Here's an illustration for clarity:
```
y-axis
|
|
5 | (5, -1)
|
4 |
|
3 |
|
2 |
|
1 |
|
0------------------------------------ x-axis
-1
0 1 2 3 4 5 6 7 8 ...
```
On the plot, the point [tex]\((5, -1)\)[/tex] is marked with an asterisk [tex]\(\)[/tex] and labeled accordingly. The gridlines and any annotations can help clearly identify the coordinates of the plotted point.
