Let's solve each distance problem using the
Distance Formula:
$$
\text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$
We'll apply this formula to each pair of points and round to the nearest hundredth when necessary.
---
1. (8, 6) and (-3, 1)
$$
\text{Distance} = \sqrt{(-3 - 8)^2 + (1 - 6)^2} = \sqrt{(-11)^2 + (-5)^2} = \sqrt{121 + 25} = \sqrt{146} \approx 12.08
$$
✔ Answer: 12.08
---
2. (5, -1) and (7, 9)
$$
\text{Distance} = \sqrt{(7 - 5)^2 + (9 - (-1))^2} = \sqrt{(2)^2 + (10)^2} = \sqrt{4 + 100} = \sqrt{104} \approx 10.20
$$
✔ Answer: 10.20
---
3. (-3, 1) and (9, 6)
$$
\text{Distance} = \sqrt{(9 - (-3))^2 + (6 - 1)^2} = \sqrt{(12)^2 + (5)^2} = \sqrt{144 + 25} = \sqrt{169} = 13.00
$$
✔ Answer: 13.00
---
4. (2, 1) and (7, 3)
$$
\text{Distance} = \sqrt{(7 - 2)^2 + (3 - 1)^2} = \sqrt{(5)^2 + (2)^2} = \sqrt{25 + 4} = \sqrt{29} \approx 5.39
$$
✔ Answer: 5.39
---
5. (-5, 3) and (7, 6)
$$
\text{Distance} = \sqrt{(7 - (-5))^2 + (6 - 3)^2} = \sqrt{(12)^2 + (3)^2} = \sqrt{144 + 9} = \sqrt{153} \approx 12.37
$$
✔ Answer: 12.37
---
6. (7, 5) and (2, 8)
$$
\text{Distance} = \sqrt{(2 - 7)^2 + (8 - 5)^2} = \sqrt{(-5)^2 + (3)^2} = \sqrt{25 + 9} = \sqrt{34} \approx 5.83
$$
✔ Answer: 5.83
---
✔ Final Answers (rounded to nearest hundredth):
| Points | Distance |
|-------|---------|
| (8,6), (-3,1) |
12.08 |
| (5,-1), (7,9) |
10.20 |
| (-3,1), (9,6) |
13.00 |
| (2,1), (7,3) |
5.39 |
| (-5,3), (7,6) |
12.37 |
| (7,5), (2,8) |
5.83 |
Let me know if you'd like a visual explanation or step-by-step breakdown for any specific pair!
Parent Tip: Review the logic above to help your child master the concept of distance on the coordinate plane worksheet.
