Math worksheet for finding the distance between two points with coordinate pairs.

Let’s solve each problem step by step using the distance formula:

> Distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:
> $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

We’ll calculate each one carefully and round to two decimal places.

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1) (-1, -7), (-9, -8)
$x_1 = -1, y_1 = -7$
$x_2 = -9, y_2 = -8$
Difference in x: $-9 - (-1) = -8$ → squared = 64
Difference in y: $-8 - (-7) = -1$ → squared = 1
Sum = 65 → $\sqrt{65} ≈ 8.06$

✔ Answer: 8.06

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2) (-3, 8), (2, 3)
$x_1 = -3, y_1 = 8$
$x_2 = 2, y_2 = 3$
Δx = 2 - (-3) = 5 → 25
Δy = 3 - 8 = -5 → 25
Sum = 50 → $\sqrt{50} ≈ 7.07$

✔ Answer: 7.07

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3) (4, 0), (0, 10)
Δx = 0 - 4 = -4 → 16
Δy = 10 - 0 = 10 → 100
Sum = 116 → $\sqrt{116} ≈ 10.77$

✔ Answer: 10.77

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4) (2, 8), (-5, 6)
Δx = -5 - 2 = -7 → 49
Δy = 6 - 8 = -2 → 4
Sum = 53 → $\sqrt{53} ≈ 7.28$

✔ Answer: 7.28

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5) (-10, -4), (0, 2)
Δx = 0 - (-10) = 10 → 100
Δy = 2 - (-4) = 6 → 36
Sum = 136 → $\sqrt{136} ≈ 11.66$

✔ Answer: 11.66

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6) (7, 5), (-6, -5)
Δx = -6 - 7 = -13 → 169
Δy = -5 - 5 = -10 → 100
Sum = 269 → $\sqrt{269} ≈ 16.40$

✔ Answer: 16.40

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7) (-4, 1), (-2, -7)
Δx = -2 - (-4) = 2 → 4
Δy = -7 - 1 = -8 → 64
Sum = 68 → $\sqrt{68} ≈ 8.25$

✔ Answer: 8.25

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8) (8, -1), (3, -9)
Δx = 3 - 8 = -5 → 25
Δy = -9 - (-1) = -8 → 64
Sum = 89 → $\sqrt{89} ≈ 9.43$

✔ Answer: 9.43

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9) (9, 6), (6, 10)
Δx = 6 - 9 = -3 → 9
Δy = 10 - 6 = 4 → 16
Sum = 25 → $\sqrt{25} = 5.00$

✔ Answer: 5.00

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10) (-4, -9), (3, 1)
Δx = 3 - (-4) = 7 → 49
Δy = 1 - (-9) = 10 → 100
Sum = 149 → $\sqrt{149} ≈ 12.21$

✔ Answer: 12.21

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Final Answer:
1) 8.06
2) 7.07
3) 10.77
4) 7.28
5) 11.66
6) 16.40
7) 8.25
8) 9.43
9) 5.00
10) 12.21