Find the distance between each pair of points on this math worksheet.

To find the distance between two points in a coordinate plane, we use the distance formula:

$$
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

Where:
- $(x_1, y_1)$ and $(x_2, y_2)$ are the coordinates of the two points.
- $d$ is the distance between them.

We will apply this formula to each pair of points and round the answers to two decimal places.

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1) $(-1, -7)$ and $(-9, -8)$

$$
d = \sqrt{(-9 - (-1))^2 + (-8 - (-7))^2} = \sqrt{(-8)^2 + (-1)^2} = \sqrt{64 + 1} = \sqrt{65} \approx 8.06
$$

✔ Answer: 8.06

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2) $(-3, 8)$ and $(2, 3)$

$$
d = \sqrt{(2 - (-3))^2 + (3 - 8)^2} = \sqrt{(5)^2 + (-5)^2} = \sqrt{25 + 25} = \sqrt{50} \approx 7.07
$$

✔ Answer: 7.07

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3) $(4, 0)$ and $(0, 10)$

$$
d = \sqrt{(0 - 4)^2 + (10 - 0)^2} = \sqrt{(-4)^2 + 10^2} = \sqrt{16 + 100} = \sqrt{116} \approx 10.77
$$

✔ Answer: 10.77

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4) $(2, 8)$ and $(-5, 6)$

$$
d = \sqrt{(-5 - 2)^2 + (6 - 8)^2} = \sqrt{(-7)^2 + (-2)^2} = \sqrt{49 + 4} = \sqrt{53} \approx 7.28
$$

✔ Answer: 7.28

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5) $(-10, -4)$ and $(0, 2)$

$$
d = \sqrt{(0 - (-10))^2 + (2 - (-4))^2} = \sqrt{(10)^2 + (6)^2} = \sqrt{100 + 36} = \sqrt{136} \approx 11.66
$$

✔ Answer: 11.66

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6) $(7, 5)$ and $(-6, -5)$

$$
d = \sqrt{(-6 - 7)^2 + (-5 - 5)^2} = \sqrt{(-13)^2 + (-10)^2} = \sqrt{169 + 100} = \sqrt{269} \approx 16.40
$$

✔ Answer: 16.40

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7) $(-4, 1)$ and $(-2, -7)$

$$
d = \sqrt{(-2 - (-4))^2 + (-7 - 1)^2} = \sqrt{(2)^2 + (-8)^2} = \sqrt{4 + 64} = \sqrt{68} \approx 8.25
$$

✔ Answer: 8.25

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8) $(8, -1)$ and $(3, -9)$

$$
d = \sqrt{(3 - 8)^2 + (-9 - (-1))^2} = \sqrt{(-5)^2 + (-8)^2} = \sqrt{25 + 64} = \sqrt{89} \approx 9.43
$$

✔ Answer: 9.43

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9) $(9, 6)$ and $(6, 10)$

$$
d = \sqrt{(6 - 9)^2 + (10 - 6)^2} = \sqrt{(-3)^2 + (4)^2} = \sqrt{9 + 16} = \sqrt{25} = 5.00
$$

✔ Answer: 5.00

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10) $(-4, -9)$ and $(3, 1)$

$$
d = \sqrt{(3 - (-4))^2 + (1 - (-9))^2} = \sqrt{(7)^2 + (10)^2} = \sqrt{49 + 100} = \sqrt{149} \approx 12.21
$$

✔ Answer: 12.21

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✔ Final Answers (Rounded to Two Decimal Places):

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

Let me know if you'd like these shown in a table or need help visualizing any of them!