truct a coordinate system on the line. Choose an interval length that allows each of the po ribed to be plotted. Plot and label the points. Point $$ A $$ is located 1 unit from 0 . Point $$ B $$ is located at $$ 2 \frac{1}{4} $$. Point $$ C $$ is located $$ \frac{1}{2} $$ unit farther from 0 than point $$ A $$. Point located $$ \frac{1}{2} $$ unit closer to 0 than point $$ B $$.

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To construct a coordinate system on a line and plot the points as described, let's follow these steps:

1. **Identify the points based on the given conditions:**
   - Point $$ A $$ is located 1 unit from 0. Therefore, $$ A = 1 $$.
   - Point $$ B $$ is located at $$ 2 \frac{1}{4} $$. This can be converted to an improper fraction: 
     $$
     B = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4}
     $$
   - Point $$ C $$ is located $$ \frac{1}{2} $$ unit farther from 0 than point $$ A $$. Since $$ A = 1 $$:
     $$
     C = A + \frac{1}{2} = 1 + \frac{1}{2} = \frac{2}{2} + \frac{1}{2} = \frac{3}{2}
     $$
   - The last point is located $$ \frac{1}{2} $$ unit closer to 0 than point $$ B $$:
     $$
     D = B - \frac{1}{2} = \frac{9}{4} - \frac{2}{4} = \frac{7}{4}
     $$

2. **Summarize the points:**
   - $$ A = 1 $$
   - $$ B = \frac{9}{4} $$
   - $$ C = \frac{3}{2} $$
   - $$ D = \frac{7}{4} $$

3. **Choose an interval length for the coordinate system:**
   - Since the largest point is $$ B = \frac{9}{4} = 2.25 $$, we can choose an interval of 1 unit for simplicity. This will allow us to plot points from 0 to 3.

4. **Plot the points on the coordinate system:**
   - The points will be plotted as follows:
     - $$ A $$ at $$ 1 $$
     - $$ B $$ at $$ 2.25 $$ (or $$ \frac{9}{4} $$)
     - $$ C $$ at $$ 1.5 $$ (or $$ \frac{3}{2} $$)
     - $$ D $$ at $$ 1.75 $$ (or $$ \frac{7}{4} $$)

5. **Label the points:**
   - On the number line, we will label the points accordingly.

Now, let's summarize the coordinates for plotting:
- $$ A(1) $$
- $$ B(2.25) $$
- $$ C(1.5) $$
- $$ D(1.75) $$

The coordinate system can be visualized as follows:

```
0    1    2    3
|----|----|----|
     A    C    D    B
```

- $$ A $$ is at 1
- $$ C $$ is at 1.5
- $$ D $$ is at 1.75
- $$ B $$ is at 2.25

This completes the plotting and labeling of the points on the coordinate system.
Here are the points plotted on the coordinate system: - Point $$ A $$ at 1 - Point $$ B $$ at 2.25 - Point $$ C $$ at 1.5 - Point $$ D $$ at 1.75

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