Labeling parts of a coordinate plane and identifying quadrants for given points.

Let's solve this step by step.

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Part 1: Label the parts of the coordinate plane

We are given a blank coordinate plane and asked to label:

1. X-axis – The horizontal axis (left-right line).
2. Y-axis – The vertical axis (up-down line).
3. Origin – The point where the X-axis and Y-axis intersect, which is at (0, 0).
4. Quadrant I – Top right quadrant (positive x, positive y).
5. Quadrant II – Top left quadrant (negative x, positive y).
6. Quadrant III – Bottom left quadrant (negative x, negative y).
7. Quadrant IV – Bottom right quadrant (positive x, negative y).

✔ So on the graph:
- Draw or write "X-axis" along the horizontal line.
- Write "Y-axis" along the vertical line.
- Mark "Origin" at (0, 0).
- Label each quadrant accordingly.

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Part 2: Determine the quadrant for each point

To determine the quadrant of a point (x, y), use the signs of the coordinates:

| Quadrant | x-sign | y-sign |
|---------|--------|--------|
| I | + | + |
| II | - | + |
| III | - | - |
| IV | + | - |

Now let’s go through each point:

1. (-3, 2)
- x = -3 (negative), y = 2 (positive) → Quadrant II

2. (-4, -5)
- x = -4 (negative), y = -5 (negative) → Quadrant III

3. (2, -3)
- x = 2 (positive), y = -3 (negative) → Quadrant IV

4. (5, -4)
- x = 5 (positive), y = -4 (negative) → Quadrant IV

5. (5, 2)
- x = 5 (positive), y = 2 (positive) → Quadrant I

6. (-4, 1)
- x = -4 (negative), y = 1 (positive) → Quadrant II

7. (-10, -3)
- x = -10 (negative), y = -3 (negative) → Quadrant III

8. (13, 15)
- x = 13 (positive), y = 15 (positive) → Quadrant I

9. (-4, -8)
- x = -4 (negative), y = -8 (negative) → Quadrant III

10. (9, -2)
- x = 9 (positive), y = -2 (negative) → Quadrant IV

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✔ Final Answers:

Label the quadrants for the points:

1. (-3, 2) → Quadrant II
2. (-4, -5) → Quadrant III
3. (2, -3) → Quadrant IV
4. (5, -4) → Quadrant IV
5. (5, 2) → Quadrant I
6. (-4, 1) → Quadrant II
7. (-10, -3) → Quadrant III
8. (13, 15) → Quadrant I
9. (-4, -8) → Quadrant III
10. (9, -2) → Quadrant IV

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Let me know if you'd like a visual explanation or help labeling the graph!