Practice worksheet for calculating distance and midpoint between coordinate points.

It looks like you've uploaded a worksheet titled "Distance and Midpoint - Practice 1" with two sections:

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Section 1: Distance Between Two Points

Instructions: For questions 1–10, find the distance between points A and B. Give answers to the nearest tenth.

The formula for distance between two points $ A(x_1, y_1) $ and $ B(x_2, y_2) $ is:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Let’s solve each one step by step.

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#### 1. A (7, 3), B (5, 4)
$$
= \sqrt{(5 - 7)^2 + (4 - 3)^2} = \sqrt{(-2)^2 + (1)^2} = \sqrt{4 + 1} = \sqrt{5} \approx 2.2
$$

✔ Answer: 2.2

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#### 2. A (5, -8), B (5, 4)
Same x-values → vertical line
$$
= |4 - (-8)| = |12| = 12.0
$$

✔ Answer: 12.0

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#### 3. A (6, 7), B (0, 7)
Same y-values → horizontal line
$$
= |6 - 0| = 6.0
$$

✔ Answer: 6.0

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#### 4. A (6, 7), B (1, 1)
$$
= \sqrt{(1 - 6)^2 + (1 - 7)^2} = \sqrt{(-5)^2 + (-6)^2} = \sqrt{25 + 36} = \sqrt{61} \approx 7.8
$$

✔ Answer: 7.8

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#### 5. A (5, 1), B (1, 1)
Same y-values → horizontal
$$
= |5 - 1| = 4.0
$$

✔ Answer: 4.0

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#### 6. A (1, 7), B (4, 0)
$$
= \sqrt{(4 - 1)^2 + (0 - 7)^2} = \sqrt{(3)^2 + (-7)^2} = \sqrt{9 + 49} = \sqrt{58} \approx 7.6
$$

✔ Answer: 7.6

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#### 7. A (4, -6), B (1, -1)
$$
= \sqrt{(1 - 4)^2 + (-1 + 6)^2} = \sqrt{(-3)^2 + (5)^2} = \sqrt{9 + 25} = \sqrt{34} \approx 5.8
$$

✔ Answer: 5.8

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#### 8. A (7, 7), B (7, 8)
Same x-values → vertical
$$
= |8 - 7| = 1.0
$$

✔ Answer: 1.0

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#### 9. A (4, -6), B (2, 7)
$$
= \sqrt{(2 - 4)^2 + (7 + 6)^2} = \sqrt{(-2)^2 + (13)^2} = \sqrt{4 + 169} = \sqrt{173} \approx 13.5
$$

✔ Answer: 13.5

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#### 10. A (3, -1), B (2, -6)
$$
= \sqrt{(2 - 3)^2 + (-6 + 1)^2} = \sqrt{(-1)^2 + (-5)^2} = \sqrt{1 + 25} = \sqrt{26} \approx 5.1
$$

✔ Answer: 5.1

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✔ Section 1 Answers (rounded to nearest tenth):

1. 2.2
2. 12.0
3. 6.0
4. 7.8
5. 4.0
6. 7.6
7. 5.8
8. 1.0
9. 13.5
10. 5.1

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Section 2: Midpoint of a Segment

Instructions: For questions 11–20, find the midpoint of the line segment with the given endpoints.

Midpoint Formula:
$$
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
$$

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#### 11. (3, 0), (1, 8)
$$
= \left( \frac{3+1}{2}, \frac{0+8}{2} \right) = (2, 4)
$$

✔ Answer: (2, 4)

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#### 12. (10, 8), (6, 2)
$$
= \left( \frac{10+6}{2}, \frac{8+2}{2} \right) = (8, 5)
$$

✔ Answer: (8, 5)

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#### 13. (7, 4), (7, -8)
$$
= \left( \frac{7+7}{2}, \frac{4+(-8)}{2} \right) = (7, -2)
$$

✔ Answer: (7, -2)

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#### 14. (4, -6), (7, 4)
$$
= \left( \frac{4+7}{2}, \frac{-6+4}{2} \right) = (5.5, -1)
$$

✔ Answer: (5.5, -1)

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#### 15. (-1, 5), (3, 3)
$$
= \left( \frac{-1+3}{2}, \frac{5+3}{2} \right) = (1, 4)
$$

✔ Answer: (1, 4)

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#### 16. (4, 9), (8, 1)
$$
= \left( \frac{4+8}{2}, \frac{9+1}{2} \right) = (6, 5)
$$

✔ Answer: (6, 5)

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#### 17. (6, -1), (4, 4)
$$
= \left( \frac{6+4}{2}, \frac{-1+4}{2} \right) = (5, 1.5)
$$

✔ Answer: (5, 1.5)

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#### 18. (8, -1), (8, 2)
Same x-values
$$
= \left( \frac{8+8}{2}, \frac{-1+2}{2} \right) = (8, 0.5)
$$

✔ Answer: (8, 0.5)

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#### 19. (4, 4), (2, 4)
Same y-values
$$
= \left( \frac{4+2}{2}, \frac{4+4}{2} \right) = (3, 4)
$$

✔ Answer: (3, 4)

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#### 20. (4, -6), (2, 0)
$$
= \left( \frac{4+2}{2}, \frac{-6+0}{2} \right) = (3, -3)
$$

✔ Answer: (3, -3)

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✔ Section 2 Answers:

11. (2, 4)
12. (8, 5)
13. (7, -2)
14. (5.5, -1)
15. (1, 4)
16. (6, 5)
17. (5, 1.5)
18. (8, 0.5)
19. (3, 4)
20. (3, -3)

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✔ Final Summary:

Section 1 – Distance (to nearest tenth):
1. 2.2
2. 12.0
3. 6.0
4. 7.8
5. 4.0
6. 7.6
7. 5.8
8. 1.0
9. 13.5
10. 5.1

Section 2 – Midpoint:
11. (2, 4)
12. (8, 5)
13. (7, -2)
14. (5.5, -1)
15. (1, 4)
16. (6, 5)
17. (5, 1.5)
18. (8, 0.5)
19. (3, 4)
20. (3, -3)

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