To solve this problem, we need to calculate the distance between each pair of points using the Pythagorean distance formula:
> d(x, y) = √[(x₂ - x₁)² + (y₂ - y₁)²]
This means:
- Take the difference in x-coordinates, square it.
- Take the difference in y-coordinates, square it.
- Add those two squares.
- Take the square root of the sum.
- Round to the nearest hundredth (two decimal places).
We’ll go point by point, reading coordinates from the grid.
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Step 1: Find coordinates for each point
From the graph:
- A = (8, 3)
- B = (-1, -7)
- C = (-6, 9)
- D = (-1, 3)
- E = (-2, 0)
- F = (-9, -4)
- G = (-1, -3)
- H = (-1, -10)
- J = (3, -5)
- K = (1, 3)
- M = (-4, -6)
- N = (-2, -9)
- P = (4, 10)
- Q = (-6, 8)
- R = (4, 3)
- S = (-5, 0)
- T = (8, -10)
- V = (7, -4)
- W = (-3, -9)
- Z = (1, 0)
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Step 2: Calculate each distance
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d(A, B) → A(8,3), B(-1,-7)
Δx = -1 - 8 = -9 → (-9)² = 81
Δy = -7 - 3 = -10 → (-10)² = 100
Sum = 81 + 100 = 181
√181 ≈ 13.4536 →
13.45
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d(C, D) → C(-6,9), D(-1,3)
Δx = -1 - (-6) = 5 → 25
Δy = 3 - 9 = -6 → 36
Sum = 61
√61 ≈ 7.8102 →
7.81
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d(E, F) → E(-2,0), F(-9,-4)
Δx = -9 - (-2) = -7 → 49
Δy = -4 - 0 = -4 → 16
Sum = 65
√65 ≈ 8.0623 →
8.06
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d(G, H) → G(-1,-3), H(-1,-10)
Δx = -1 - (-1) = 0 → 0
Δy = -10 - (-3) = -7 → 49
Sum = 49
√49 = 7.00 →
7.00
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d(J, K) → J(3,-5), K(1,3)
Δx = 1 - 3 = -2 → 4
Δy = 3 - (-5) = 8 → 64
Sum = 68
√68 ≈ 8.2462 →
8.25
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d(M, N) → M(-4,-6), N(-2,-9)
Δx = -2 - (-4) = 2 → 4
Δy = -9 - (-6) = -3 → 9
Sum = 13
√13 ≈ 3.6056 →
3.61
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d(P, Q) → P(4,10), Q(-6,8)
Δx = -6 - 4 = -10 → 100
Δy = 8 - 10 = -2 → 4
Sum = 104
√104 ≈ 10.1980 →
10.20
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d(R, S) → R(4,3), S(-5,0)
Δx = -5 - 4 = -9 → 81
Δy = 0 - 3 = -3 → 9
Sum = 90
√90 ≈ 9.4868 →
9.49
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d(T, V) → T(8,-10), V(7,-4)
Δx = 7 - 8 = -1 → 1
Δy = -4 - (-10) = 6 → 36
Sum = 37
√37 ≈ 6.0828 →
6.08
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d(W, Z) → W(-3,-9), Z(1,0)
Δx = 1 - (-3) = 4 → 16
Δy = 0 - (-9) = 9 → 81
Sum = 97
√97 ≈ 9.8489 →
9.85
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All calculations verified. Rounded to nearest hundredth.
Final Answer:
d(A, B) = 13.45
d(C, D) = 7.81
d(E, F) = 8.06
d(G, H) = 7.00
d(J, K) = 8.25
d(M, N) = 3.61
d(P, Q) = 10.20
d(R, S) = 9.49
d(T, V) = 6.08
d(W, Z) = 9.85
Parent Tip: Review the logic above to help your child master the concept of pythagorean theorem on coordinate plane worksheet.
