Coordinate Graphing Worksheet for Writing Ordered Pairs and Answering Distance and Quadrant Questions.

Let's solve the coordinate graphing problem step by step.

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Step 1: Identify the coordinates of each point

We are given a coordinate grid with points labeled A through H. We need to determine the ordered pairs (x, y) for each point.

Looking at the graph:

- A: x = -4, y = 3 → (-4, 3)
- B: x = -5, y = 5 → (-5, 5)
- C: x = 3, y = 2 → (3, 2)
- D: x = 3, y = 5 → (3, 5)
- E: x = -4, y = -4 → (-4, -4)
- F: x = 5, y = 3 → (5, 3)
- G: x = 4, y = -2 → (4, -2)
- H: x = -2, y = -1 → (-2, -1)

So fill in the blanks:
```
A( -4 , 3 )
B( -5 , 5 )
C( 3 , 2 )
D( 3 , 5 )
E( -4 , -4 )
F( 5 , 3 )
G( 4 , -2 )
H( -2 , -1 )
```

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Step 2: Answer the questions

#### 1) The distance between point D and G is ________

- Point D: (3, 5)
- Point G: (4, -2)

Use the distance formula:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

$$
= \sqrt{(4 - 3)^2 + (-2 - 5)^2} = \sqrt{(1)^2 + (-7)^2} = \sqrt{1 + 49} = \sqrt{50} = 5\sqrt{2} \approx 7.07
$$

But since this is likely meant for basic coordinate skills, let’s see if we can do it simpler.

Alternatively, you can count the horizontal and vertical distances:

- Horizontal: from x = 3 to x = 4 → 1 unit
- Vertical: from y = 5 to y = -2 → 7 units down

So the distance is:
$$
\sqrt{1^2 + 7^2} = \sqrt{50} = 5\sqrt{2}
$$

✔ So the answer is $5\sqrt{2}$ or approximately 7.07, but since it's a worksheet, maybe just leave as $\sqrt{50}$ or 5√2.

But often in such worksheets, they expect exact value, so:

👉 Answer: $5\sqrt{2}$

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#### 2) The quadrant of point H is ________

Point H: (-2, -1)

- x = -2 (negative)
- y = -1 (negative)

→ This is Quadrant III

👉 Answer: Quadrant III

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#### 3) The distance between point B and E is ________

- B: (-5, 5)
- E: (-4, -4)

Use distance formula:
$$
\sqrt{(-4 - (-5))^2 + (-4 - 5)^2} = \sqrt{(1)^2 + (-9)^2} = \sqrt{1 + 81} = \sqrt{82}
$$

So the distance is $\sqrt{82}$ ≈ 9.06

👉 Answer: $\sqrt{82}$

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#### 4) The quadrant of point B is ________

Point B: (-5, 5)

- x = -5 (negative)
- y = 5 (positive)

→ This is Quadrant II

👉 Answer: Quadrant II

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#### 5) The point located at (-3, -2) is ________

Look at the graph: Find where x = -3 and y = -2.

On the grid:
- Move left 3 units from origin (x = -3)
- Down 2 units (y = -2)

This point is not labeled, but check nearby points:

- H is at (-2, -1)
- E is at (-4, -4)
- No point is labeled at (-3, -2)

So, the answer should be: There is no labeled point at (-3, -2)

But wait — perhaps we misread?

Let’s double-check the grid:

At x = -3, y = -2 → Is there a dot? Looking at the image:

- At x = -3, y = -2 → There is no point labeled.
- The closest labeled points are:
- H at (-2, -1)
- E at (-4, -4)
- F at (5,3), etc.

So no point is marked at (-3, -2). Therefore, the answer is:

👉 No point is labeled at (-3, -2)

But the question says "The point located at (-3, -2) is ________" — so perhaps it's asking us to name it or say it's unlabeled.

Since all other points are labeled, and none are at (-3, -2), we conclude:

👉 Answer: There is no labeled point at (-3, -2)

Or possibly, the student is expected to say "none" or "not labeled".

But in some cases, maybe the point is implied? Let's recheck.

Wait — looking again: Is there a point near (-3, -2)? No.

So final answer: None / Not labeled

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✔ Final Answers:

Ordered Pairs:
- A(-4, 3)
- B(-5, 5)
- C(3, 2)
- D(3, 5)
- E(-4, -4)
- F(5, 3)
- G(4, -2)
- H(-2, -1)

Questions:

1) Distance between D and G: $5\sqrt{2}$
2) Quadrant of H: Quadrant III
3) Distance between B and E: $\sqrt{82}$
4) Quadrant of B: Quadrant II
5) The point at (-3, -2): Not labeled (or "none")

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