Distance Formula Worksheets - Free Printable

It looks like you've uploaded a worksheet titled "Distance Formula" that includes a sample problem and several practice problems. Let's solve the example and then go through each of the practice problems step by step.

---

🔹 Example Problem (Given):

Find the distance between the points (3, -1) and (5, 2).

We use the distance formula:

$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Plug in the values:
- $ x_1 = 3 $, $ y_1 = -1 $
- $ x_2 = 5 $, $ y_2 = 2 $

$$
= \sqrt{(5 - 3)^2 + (2 - (-1))^2}
= \sqrt{(2)^2 + (3)^2}
= \sqrt{4 + 9}
= \sqrt{13} \approx 3.61 \text{ units}
$$

✔ So, the answer is √13 ≈ 3.61 units, which matches what’s shown.

---

Now let’s solve each of the practice problems using the same formula.

---

✔ Problem 1: (3, 8), (5, 7)

$$
\sqrt{(5 - 3)^2 + (7 - 8)^2} = \sqrt{(2)^2 + (-1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.24
$$

🔹 Answer: $ \sqrt{5} \approx 2.24 $

---

✔ Problem 2: (30, 4), (-4, -4)

$$
\sqrt{(-4 - 30)^2 + (-4 - 4)^2} = \sqrt{(-34)^2 + (-8)^2} = \sqrt{1156 + 64} = \sqrt{1220}
$$

Simplify:
- $ \sqrt{1220} \approx 34.93 $

🔹 Answer: $ \sqrt{1220} \approx 34.93 $

---

✔ Problem 3: (2, 1), (3, 2)

$$
\sqrt{(3 - 2)^2 + (2 - 1)^2} = \sqrt{1^2 + 1^2} = \sqrt{1 + 1} = \sqrt{2} \approx 1.41
$$

🔹 Answer: $ \sqrt{2} \approx 1.41 $

---

✔ Problem 4: (10, 5), (6, 8)

$$
\sqrt{(6 - 10)^2 + (8 - 5)^2} = \sqrt{(-4)^2 + (3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5
$$

🔹 Answer: $ 5 $

---

✔ Problem 5: (-2, -2), (6, 6)

$$
\sqrt{(6 - (-2))^2 + (6 - (-2))^2} = \sqrt{(8)^2 + (8)^2} = \sqrt{64 + 64} = \sqrt{128}
$$

Simplify:
- $ \sqrt{128} = \sqrt{64 \cdot 2} = 8\sqrt{2} \approx 11.31 $

🔹 Answer: $ 8\sqrt{2} \approx 11.31 $

---

✔ Problem 6: (4, 7), (2, 5)

$$
\sqrt{(2 - 4)^2 + (5 - 7)^2} = \sqrt{(-2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} = 2\sqrt{2} \approx 2.83
$$

🔹 Answer: $ 2\sqrt{2} \approx 2.83 $

---

✔ Problem 7: (-1, 5), (-4, -4)

$$
\sqrt{(-4 - (-1))^2 + (-4 - 5)^2} = \sqrt{(-3)^2 + (-9)^2} = \sqrt{9 + 81} = \sqrt{90}
$$

Simplify:
- $ \sqrt{90} = \sqrt{9 \cdot 10} = 3\sqrt{10} \approx 9.49 $

🔹 Answer: $ 3\sqrt{10} \approx 9.49 $

---

✔ Problem 8: (5, 0), (-1, 5)

$$
\sqrt{(-1 - 5)^2 + (5 - 0)^2} = \sqrt{(-6)^2 + (5)^2} = \sqrt{36 + 25} = \sqrt{61} \approx 7.81
$$

🔹 Answer: $ \sqrt{61} \approx 7.81 $

---

✔ Final Answers Summary:

| Problem | Points | Distance |
|--------|--------|----------|
| 1 | (3,8), (5,7) | $ \sqrt{5} \approx 2.24 $ |
| 2 | (30,4), (-4,-4) | $ \sqrt{1220} \approx 34.93 $ |
| 3 | (2,1), (3,2) | $ \sqrt{2} \approx 1.41 $ |
| 4 | (10,5), (6,8) | $ 5 $ |
| 5 | (-2,-2), (6,6) | $ 8\sqrt{2} \approx 11.31 $ |
| 6 | (4,7), (2,5) | $ 2\sqrt{2} \approx 2.83 $ |
| 7 | (-1,5), (-4,-4) | $ 3\sqrt{10} \approx 9.49 $ |
| 8 | (5,0), (-1,5) | $ \sqrt{61} \approx 7.81 $ |

---

Let me know if you'd like this formatted as a printable PDF or need help with graphing these points!