Let’s solve each problem step by step using the 3D distance formula:
Formula:
> d = √[(x₂ – x₁)² + (y₂ – y₁)² + (z₂ – z₁)²]
We’ll plug in the coordinates for each pair of points, calculate the differences, square them, add, and take the square root. Round to 2 decimal places if needed.
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1. (0,0,0) and (3,4,12)
d = √[(3–0)² + (4–0)² + (12–0)²]
= √[9 + 16 + 144]
= √169 =
13.00
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2. (4,–3,6) and (1,0,17)
d = √[(1–4)² + (0–(–3))² + (17–6)²]
= √[(-3)² + (3)² + (11)²]
= √[9 + 9 + 121] = √139 ≈
11.79
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3. (6,5,4) and (10,9,8)
d = √[(10–6)² + (9–5)² + (8–4)²]
= √[16 + 16 + 16] = √48 ≈
6.93
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4. (1,1,1) and (10,10,10)
d = √[(10–1)² + (10–1)² + (10–1)²]
= √[81 + 81 + 81] = √243 ≈
15.59
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5. (–4,–5,–19) and (8,3,12)
d = √[(8–(–4))² + (3–(–5))² + (12–(–19))²]
= √[(12)² + (8)² + (31)²]
= √[144 + 64 + 961] = √1169 ≈
34.19
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6. (5,5,18) and (5,5,–8)
d = √[(5–5)² + (5–5)² + (–8–18)²]
= √[0 + 0 + (–26)²] = √676 =
26.00
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7. (3,6,1) and (1,6,3)
d = √[(1–3)² + (6–6)² + (3–1)²]
= √[4 + 0 + 4] = √8 ≈
2.83
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8. (9,6,3) and (–9,–6,–3)
d = √[(–9–9)² + (–6–6)² + (–3–3)²]
= √[(–18)² + (–12)² + (–6)²]
= √[324 + 144 + 36] = √504 ≈
22.45
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Final Answer:
1. 13.00
2. 11.79
3. 6.93
4. 15.59
5. 34.19
6. 26.00
7. 2.83
8. 22.45
Parent Tip: Review the logic above to help your child master the concept of geometry distance formula worksheet.
