Let’s solve each problem step by step using the
Distance Formula:
> Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
We’ll plug in the coordinates for each pair of points, calculate carefully, and round to two decimal places if needed.
---
1) Points: (1, 3), (5, 7)
x₁=1, y₁=3; x₂=5, y₂=7
→ (5 - 1)² = 4² = 16
→ (7 - 3)² = 4² = 16
→ Sum = 16 + 16 = 32
→ √32 ≈ 5.66 units
✔
---
2) Points: (-8, -9), (-4, -10)
x₁=-8, y₁=-9; x₂=-4, y₂=-10
→ (-4 - (-8))² = (4)² = 16
→ (-10 - (-9))² = (-1)² = 1
→ Sum = 16 + 1 = 17
→ √17 ≈ 4.12 units
✔
---
3) Points: (10, 6), (1, -4)
x₁=10, y₁=6; x₂=1, y₂=-4
→ (1 - 10)² = (-9)² = 81
→ (-4 - 6)² = (-10)² = 100
→ Sum = 81 + 100 = 181
→ √181 ≈ 13.45 units
✔
---
4) Points: (3, 2), (8, 2)
x₁=3, y₁=2; x₂=8, y₂=2
→ (8 - 3)² = 5² = 25
→ (2 - 2)² = 0² = 0
→ Sum = 25 + 0 = 25
→ √25 = 5 units
✔
---
5) Points: (9, -3), (-1, 8)
x₁=9, y₁=-3; x₂=-1, y₂=8
→ (-1 - 9)² = (-10)² = 100
→ (8 - (-3))² = (11)² = 121
→ Sum = 100 + 121 = 221
→ √221 ≈ 14.87 units
✔
---
6) Points: (10, 0), (0, 4)
x₁=10, y₁=0; x₂=0, y₂=4
→ (0 - 10)² = (-10)² = 100
→ (4 - 0)² = 4² = 16
→ Sum = 100 + 16 = 116
→ √116 ≈ 10.77 units
✔
---
7) Points: (-7, -2), (6, 9)
x₁=-7, y₁=-2; x₂=6, y₂=9
→ (6 - (-7))² = (13)² = 169
→ (9 - (-2))² = (11)² = 121
→ Sum = 169 + 121 = 290
→ √290 ≈ 17.03 units
✔
---
8) Points: (-6, 5), (8, -3)
x₁=-6, y₁=5; x₂=8, y₂=-3
→ (8 - (-6))² = (14)² = 196
→ (-3 - 5)² = (-8)² = 64
→ Sum = 196 + 64 = 260
→ √260 ≈ 16.12 units
✔
---
9) Points: (-5, -6), (-9, -4)
x₁=-5, y₁=-6; x₂=-9, y₂=-4
→ (-9 - (-5))² = (-4)² = 16
→ (-4 - (-6))² = (2)² = 4
→ Sum = 16 + 4 = 20
→ √20 ≈ 4.47 units
✔
---
10) Points: (2, 0), (-7, 1)
x₁=2, y₁=0; x₂=-7, y₂=1
→ (-7 - 2)² = (-9)² = 81
→ (1 - 0)² = 1² = 1
→ Sum = 81 + 1 = 82
→ √82 ≈ 9.06 units
✔
---
All calculations match the provided answer key. Each distance was computed correctly using the formula and rounded appropriately.
Final Answer:
1) 5.66 units
2) 4.12 units
3) 13.45 units
4) 5 units
5) 14.87 units
6) 10.77 units
7) 17.03 units
8) 16.12 units
9) 4.47 units
10) 9.06 units
Parent Tip: Review the logic above to help your child master the concept of distance formula worksheet.
