To answer this question, let's carefully analyze each step and identify the coordinate plane that shows the polygon with the vertices at [tex]\((-5, 5)\)[/tex], [tex]\((2, 4)\)[/tex], [tex]\((6, -2)\)[/tex], and [tex]\((-3, -6)\)[/tex].
### Step-by-Step Solution
1. Identify the Coordinates:
- Vertex 1: [tex]\((-5, 5)\)[/tex]
- Vertex 2: [tex]\((2, 4)\)[/tex]
- Vertex 3: [tex]\((6, -2)\)[/tex]
- Vertex 4: [tex]\((-3, -6)\)[/tex]
2. Plotting the Coordinates:
- [tex]\((-5, 5)\)[/tex]: This point lies 5 units to the left of the y-axis and 5 units above the x-axis.
- [tex]\((2, 4)\)[/tex]: This point lies 2 units to the right of the y-axis and 4 units above the x-axis.
- [tex]\((6, -2)\)[/tex]: This point lies 6 units to the right of the y-axis and 2 units below the x-axis.
- [tex]\((-3, -6)\)[/tex]: This point lies 3 units to the left of the y-axis and 6 units below the x-axis.
3. Examining Each Coordinate Plane Option:
- Option A:
```
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| (2,4)
| .
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```
- Option B:
```
(-5,5)
|
|
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| (2,4)
| .
|
|
|
|
```
- Option C:
```
|
|
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| (2,4)
| .
|
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```
- Option D:
```
(6,-2)
| .
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| (2,4)
| .
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| (-5,5)
|
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| (-3,-6)
| .
```
4. Selecting the Correct Coordinate Plane:
Examine each provided coordinate plane to see if it matches our vertices at [tex]\((-5, 5)\)[/tex], [tex]\((2, 4)\)[/tex], [tex]\((6, -2)\)[/tex], and [tex]\((-3, -6)\)[/tex].
Looking at Option D, it correctly plots the vertices at the correct positions:
- [tex]\((-5, 5)\)[/tex]: appears at -5 on x-axis and 5 on y-axis
- [tex]\((2, 4)\)[/tex]: appears at 2 on x-axis and 4 on y-axis
- [tex]\((6, -2)\)[/tex]: appears at 6 on x-axis and -2 on y-axis
- [tex]\((-3, -6)\)[/tex]: appears at -3 on x-axis and -6 on y-axis
Conclusion: Option D is the correct coordinate plane showing a polygon with four vertices graphed at [tex]\((-5, 5)\)[/tex], [tex]\((2, 4)\)[/tex], [tex]\((6, -2)\)[/tex], and [tex]\((-3, -6)\)[/tex].
