Quadrants Worksheets - 15 Worksheets Library - Free Printable

Let's solve the problem step by step.

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Step 1: Understand the Coordinate Plane and Quadrants

The coordinate plane is divided into four quadrants by the x-axis (horizontal) and y-axis (vertical). The quadrants are labeled counterclockwise starting from the top right:

- Quadrant I: (+, +) → both x and y are positive
- Quadrant II: (−, +) → x is negative, y is positive
- Quadrant III: (−, −) → both x and y are negative
- Quadrant IV: (+, −) → x is positive, y is negative

Also:
- The x-axis is the horizontal line.
- The y-axis is the vertical line.
- The origin is at (0, 0), where the axes intersect.

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Step 2: Fill in the Blanks on the Grid

We need to label the quadrants and the axes:

#### Axes Labels
- The horizontal axis is the x-axis.
- The vertical axis is the y-axis.

So:
- Left arrow pointing to horizontal axis → x-axis
- Upward arrow pointing to vertical axis → y-axis

#### Quadrants
Label each quadrant with its name and sign pattern:

- Top-right: Quadrant I → (+, +)
- Top-left: Quadrant II → (−, +)
- Bottom-left: Quadrant III → (−, −)
- Bottom-right: Quadrant IV → (+, −)

So fill in:

```
Quadrant I Quadrant II
( +, + ) ( −, + )
Quadrant III Quadrant IV
( −, − ) ( +, − )
```

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Step 3: Determine the Quadrant for Each Ordered Pair

Now, determine which quadrant each point lies in based on the signs of the coordinates.

| Point | x-sign | y-sign | Quadrant |
|-------|--------|--------|----------|
| (2, 5) | + | + | I |
| (2, -8) | + | − | IV |
| (-1, 3) | − | + | II |
| (-3, 6) | − | + | II |
| (-2, -8) | − | − | III |
| (-2, -6) | − | − | III |
| (-3, -5) | − | − | III |
| (1, 6) | + | + | I |

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✔ Final Answers

#### Fill in the blanks on the coordinate plane:

- Horizontal axis: x-axis
- Vertical axis: y-axis
- Quadrant I: (+, +)
- Quadrant II: (−, +)
- Quadrant III: (−, −)
- Quadrant IV: (+, −)

#### Write the quadrant for each ordered pair:

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

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📌 Summary

- Use the signs of the coordinates to determine the quadrant.
- Remember: I (+,+), II (−,+), III (−,−), IV (+,−).
- Points on the axes (like (0, 5)) are not in any quadrant — but none of these points are on the axes.

✔ All answers filled in correctly!