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.
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
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
---
✔ 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 formatted for printing!
Parent Tip: Review the logic above to help your child master the concept of distance worksheet.
