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.
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🔹 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
$\sqrt{13}$ or approximately 3.61 units, as shown.
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Now let’s solve the
practice problems one by one.
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🔹 Problem 1: Find the distance between the points:
(0, 1), (0, -4)
Use the distance formula:
$$
= \sqrt{(0 - 0)^2 + (-4 - 1)^2}
= \sqrt{0 + (-5)^2}
= \sqrt{25}
= 5
$$
✔ Answer: 5 units
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🔹 Problem 2:
(2, 1), (2, 3)
$$
= \sqrt{(2 - 2)^2 + (3 - 1)^2}
= \sqrt{0 + (2)^2}
= \sqrt{4}
= 2
$$
✔ Answer: 2 units
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🔹 Problem 3:
(6, 1), (3, 6)
$$
= \sqrt{(3 - 6)^2 + (6 - 1)^2}
= \sqrt{(-3)^2 + (5)^2}
= \sqrt{9 + 25}
= \sqrt{34} \approx 5.83
$$
✔ Answer: $\sqrt{34}$ or ≈ 5.83 units
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🔹 Problem 4:
(0, 0), (6, 8)
$$
= \sqrt{(6 - 0)^2 + (8 - 0)^2}
= \sqrt{36 + 64}
= \sqrt{100}
= 10
$$
✔ Answer: 10 units
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🔹 Problem 5:
(–1, –2), (6, 8)
$$
= \sqrt{(6 - (-1))^2 + (8 - (-2))^2}
= \sqrt{(7)^2 + (10)^2}
= \sqrt{49 + 100}
= \sqrt{149} \approx 12.21
$$
✔ Answer: $\sqrt{149}$ or ≈ 12.21 units
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🔹 Problem 6:
(4, 7), (1, 1)
$$
= \sqrt{(1 - 4)^2 + (1 - 7)^2}
= \sqrt{(-3)^2 + (-6)^2}
= \sqrt{9 + 36}
= \sqrt{45} = 3\sqrt{5} \approx 6.71
$$
✔ Answer: $\sqrt{45}$ or $3\sqrt{5}$ or ≈ 6.71 units
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🔹 Problem 7:
(–3, –2), (–8, 4)
$$
= \sqrt{(-8 - (-3))^2 + (4 - (-2))^2}
= \sqrt{(-5)^2 + (6)^2}
= \sqrt{25 + 36}
= \sqrt{61} \approx 7.81
$$
✔ Answer: $\sqrt{61}$ or ≈ 7.81 units
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🔹 Problem 8:
(0, 0), (1, 1)
$$
= \sqrt{(1 - 0)^2 + (1 - 0)^2}
= \sqrt{1 + 1}
= \sqrt{2} \approx 1.41
$$
✔ Answer: $\sqrt{2}$ or ≈ 1.41 units
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✔ Final Answers Summary:
| Problem | Points | Distance |
|--------|--------|----------|
| 1 | (0,1), (0,-4) |
5 |
| 2 | (2,1), (2,3) |
2 |
| 3 | (6,1), (3,6) |
$\sqrt{34}$ ≈ 5.83 |
| 4 | (0,0), (6,8) |
10 |
| 5 | (-1,-2), (6,8) |
$\sqrt{149}$ ≈ 12.21 |
| 6 | (4,7), (1,1) |
$\sqrt{45}$ = $3\sqrt{5}$ ≈ 6.71 |
| 7 | (-3,-2), (-8,4) |
$\sqrt{61}$ ≈ 7.81 |
| 8 | (0,0), (1,1) |
$\sqrt{2}$ ≈ 1.41 |
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Parent Tip: Review the logic above to help your child master the concept of distance formula worksheet 1.
