Quadrants Worksheets - 15 Worksheets Library - Free Printable

Let's solve this step-by-step based on the coordinate plane shown in the image.

We are given a graph with labeled points (A through P) plotted on a coordinate grid. The goal is to:

1. Write the ordered pair (x, y) for each letter.
2. Identify the quadrant where each letter is located.

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Step 1: Understanding the Coordinate Plane

- The x-axis runs horizontally (left to right).
- The y-axis runs vertically (up and down).
- The origin is at (0, 0).
- The quadrants are labeled as:
- Quadrant I: (+, +) → top-right
- Quadrant II: (−, +) → top-left
- Quadrant III: (−, −) → bottom-left
- Quadrant IV: (+, −) → bottom-right

Points on the axes are not in any quadrant (e.g., if x=0 or y=0), but since all these points appear to be off the axes, we can assign them to quadrants.

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Step 2: Identify Coordinates

We'll go point by point using the grid.

#### Point A:
- Located at x = 3, y = 5 → (3, 5)

#### Point B:
- x = -4, y = 6 → (-4, 6)

#### Point C:
- x = 1, y = 4 → (1, 4)

#### Point D:
- x = 6, y = 3 → (6, 3)

#### Point E:
- x = -6, y = 2 → (-6, 2)

#### Point F:
- x = -2, y = 3 → (-2, 3)

#### Point G:
- x = 4, y = -2 → (4, -2)

#### Point H:
- x = -5, y = -3 → (-5, -3)

#### Point I:
- x = 0, y = 4 → (0, 4) → On the y-axis → Not in a quadrant

But wait — let’s double-check. Is I really at (0, 4)? Looking at the graph:

- There's a point at (0, 4) labeled I? Wait — no, looking again...

Wait — actually, I is not at (0, 4). Let's re-express carefully.

Looking closely:

- Point I: At x = 2, y = -4 → (2, -4)

Wait — let me carefully recheck each point from the image description.

From the grid:

Let’s list all labeled points with their coordinates:

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Careful Analysis of Each Point:

1. A: At (3, 5) → Quadrant I
2. B: At (-4, 6) → Quadrant II
3. C: At (1, 4) → Quadrant I
4. D: At (6, 3) → Quadrant I
5. E: At (-6, 2) → Quadrant II
6. F: At (-2, 3) → Quadrant II
7. G: At (4, -2) → Quadrant IV
8. H: At (-5, -3) → Quadrant III
9. I: At (2, -4) → Quadrant IV
10. J: At (0, 4) → On the y-axis → Not in a quadrant (but likely considered "on axis")
But wait — is J at (0, 4)? Let’s see.

Wait — there is a point at (0, 4) labeled I?

No — looking again:

- Point I is at (2, -4)
- Point J is at (0, 4)

Wait — let’s look more precisely.

From the image:

- I: at (2, -4)
- J: at (0, 4)
- K: at (-3, -4)
- L: at (-1, -5)
- M: at (-6, -4)
- N: at (5, -4)
- O: at (3, -6)
- P: at (5, -6)

Let’s now list all points correctly:

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Final List of Points:

| Letter | Coordinates | Quadrant |
|--------|-------------|----------|
| A | (3, 5) | I |
| B | (-4, 6) | II |
| C | (1, 4) | I |
| D | (6, 3) | I |
| E | (-6, 2) | II |
| F | (-2, 3) | II |
| G | (4, -2) | IV |
| H | (-5, -3) | III |
| I | (2, -4) | IV |
| J | (0, 4) | On y-axis (no quadrant) |
| K | (-3, -4) | III |
| L | (-1, -5) | III |
| M | (-6, -4) | III |
| N | (5, -4) | IV |
| O | (3, -6) | IV |
| P | (5, -6) | IV |

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Now Answer the Questions

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Part 1: Write the ordered pair for each letter

1) A: (3, 5)
2) B: (-4, 6)
3) C: (1, 4)
4) D: (6, 3)
5) E: (-6, 2)
6) F: (-2, 3)
7) G: (4, -2)
8) H: (-5, -3)

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Part 2: Write the quadrant where the letter is located

9) I: IV
10) J: On the y-axis → Not in a quadrant → Usually written as "on axis" or "not in a quadrant"
But since the question asks for quadrant, and it's on the axis, we might say none or axis.
However, often such problems expect: "On the y-axis", but here they want quadrant.

So: Not in a quadrant → But if must choose, sometimes they consider it between II and I, but technically not in any.

However, since the problem says “write the quadrant”, and J is on the axis, we should note that.

But looking at the pattern, perhaps J is meant to be (0,4) — which is on the positive y-axis.

So answer: Not in a quadrant (or on the axis)

But since the format expects a quadrant number, maybe it's acceptable to write None.

But let's assume the expected answer is:

J: On the y-axis → But the question says “quadrant”

So best answer: None or Axis

But most worksheets accept: Not in a quadrant

However, let's check standard practice.

In many cases, points on axes are not assigned a quadrant.

So:

11) K: III
12) L: III
13) M: III
14) N: IV
15) O: IV
16) P: IV

And for J: Since it's at (0,4), it's on the positive y-axis, so not in a quadrant.

But perhaps the question expects us to say II or I, but that’s incorrect.

So safest answer: On the axis or None

But let's assume the worksheet allows "on the axis" or "not in a quadrant"

However, in many school worksheets, they may expect:

- If on y-axis: "On the y-axis"
- But here the blank is for quadrant.

So likely, J is intended to be in Quadrant I or II, but it's not.

Wait — could J be at (0,4)? Yes.

But then it's not in a quadrant.

So we must write:

> 10) J: On the y-axis (or None)

But since the instruction says "write the quadrant", and there is no quadrant for axis points, we write:

> Not in a quadrant

Alternatively, some teachers accept "axis"

But let’s go with standard.

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Final Answers:

#### Ordered Pairs:

1) A: (3, 5)
2) B: (-4, 6)
3) C: (1, 4)
4) D: (6, 3)
5) E: (-6, 2)
6) F: (-2, 3)
7) G: (4, -2)
8) H: (-5, -3)

#### Quadrants:

9) I: IV
10) J: On the y-axis (or Not in a quadrant)
11) K: III
12) L: III
13) M: III
14) N: IV
15) O: IV
16) P: IV

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Final Answer Boxed:

Since you asked to solve and explain:

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✔ Answer Key:

Ordered Pairs:

1) A: (3, 5)
2) B: (-4, 6)
3) C: (1, 4)
4) D: (6, 3)
5) E: (-6, 2)
6) F: (-2, 3)
7) G: (4, -2)
8) H: (-5, -3)

Quadrants:

9) I: IV
10) J: On the y-axis (not in a quadrant)
11) K: III
12) L: III
13) M: III
14) N: IV
15) O: IV
16) P: IV

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💡 Explanation:

- To find an ordered pair, read the x-coordinate (horizontal) first, then the y-coordinate (vertical).
- Quadrants are determined by the signs:
- I: (+, +)
- II: (−, +)
- III: (−, −)
- IV: (+, −)
- Points on the axes (like J at (0,4)) are not in any quadrant because they lie on the boundary.

Let me know if you'd like a printable version or explanation for students!