Distance between Two Points Worksheets - Free Printable

To solve the problem of finding the distance between two points, 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 the two points.

We will calculate the distance for each pair of points given in the problem and round the result to two decimal places.

---

Step-by-Step Solutions

#### 1. Points: \((-1, 7)\) and \((-9, -8)\)

Using the distance formula:
\[
d = \sqrt{((-9) - (-1))^2 + ((-8) - 7)^2}
\]
\[
d = \sqrt{((-9) + 1)^2 + ((-8) - 7)^2}
\]
\[
d = \sqrt{(-8)^2 + (-15)^2}
\]
\[
d = \sqrt{64 + 225}
\]
\[
d = \sqrt{289}
\]
\[
d = 17.00
\]

#### 2. Points: \((-3, 8)\) and \((2, 3)\)

Using the distance formula:
\[
d = \sqrt{(2 - (-3))^2 + (3 - 8)^2}
\]
\[
d = \sqrt{(2 + 3)^2 + (3 - 8)^2}
\]
\[
d = \sqrt{5^2 + (-5)^2}
\]
\[
d = \sqrt{25 + 25}
\]
\[
d = \sqrt{50}
\]
\[
d \approx 7.07
\]

#### 3. Points: \((4, 0)\) and \((0, 10)\)

Using the distance formula:
\[
d = \sqrt{(0 - 4)^2 + (10 - 0)^2}
\]
\[
d = \sqrt{(-4)^2 + 10^2}
\]
\[
d = \sqrt{16 + 100}
\]
\[
d = \sqrt{116}
\]
\[
d \approx 10.77
\]

#### 4. Points: \((2, 8)\) and \((-5, 6)\)

Using the distance formula:
\[
d = \sqrt{((-5) - 2)^2 + (6 - 8)^2}
\]
\[
d = \sqrt{((-5) - 2)^2 + (6 - 8)^2}
\]
\[
d = \sqrt{(-7)^2 + (-2)^2}
\]
\[
d = \sqrt{49 + 4}
\]
\[
d = \sqrt{53}
\]
\[
d \approx 7.28
\]

#### 5. Points: \((-10, -4)\) and \((0, 2)\)

Using the distance formula:
\[
d = \sqrt{(0 - (-10))^2 + (2 - (-4))^2}
\]
\[
d = \sqrt{(0 + 10)^2 + (2 + 4)^2}
\]
\[
d = \sqrt{10^2 + 6^2}
\]
\[
d = \sqrt{100 + 36}
\]
\[
d = \sqrt{136}
\]
\[
d \approx 11.66
\]

#### 6. Points: \((7, 5)\) and \((-6, -5)\)

Using the distance formula:
\[
d = \sqrt{((-6) - 7)^2 + ((-5) - 5)^2}
\]
\[
d = \sqrt{((-6) - 7)^2 + ((-5) - 5)^2}
\]
\[
d = \sqrt{(-13)^2 + (-10)^2}
\]
\[
d = \sqrt{169 + 100}
\]
\[
d = \sqrt{269}
\]
\[
d \approx 16.40
\]

#### 7. Points: \((-4, 1)\) and \((-2, -7)\)

Using the distance formula:
\[
d = \sqrt{((-2) - (-4))^2 + ((-7) - 1)^2}
\]
\[
d = \sqrt{((-2) + 4)^2 + ((-7) - 1)^2}
\]
\[
d = \sqrt{2^2 + (-8)^2}
\]
\[
d = \sqrt{4 + 64}
\]
\[
d = \sqrt{68}
\]
\[
d \approx 8.25
\]

#### 8. Points: \((8, -1)\) and \((3, -9)\)

Using the distance formula:
\[
d = \sqrt{(3 - 8)^2 + ((-9) - (-1))^2}
\]
\[
d = \sqrt{(3 - 8)^2 + ((-9) + 1)^2}
\]
\[
d = \sqrt{(-5)^2 + (-8)^2}
\]
\[
d = \sqrt{25 + 64}
\]
\[
d = \sqrt{89}
\]
\[
d \approx 9.43
\]

#### 9. Points: \((9, 6)\) and \((6, 10)\)

Using the distance formula:
\[
d = \sqrt{(6 - 9)^2 + (10 - 6)^2}
\]
\[
d = \sqrt{(-3)^2 + 4^2}
\]
\[
d = \sqrt{9 + 16}
\]
\[
d = \sqrt{25}
\]
\[
d = 5.00
\]

#### 10. Points: \((-4, -9)\) and \((3, 1)\)

Using the distance formula:
\[
d = \sqrt{(3 - (-4))^2 + (1 - (-9))^2}
\]
\[
d = \sqrt{(3 + 4)^2 + (1 + 9)^2}
\]
\[
d = \sqrt{7^2 + 10^2}
\]
\[
d = \sqrt{49 + 100}
\]
\[
d = \sqrt{149}
\]
\[
d \approx 12.21
\]

---

Final Answers

\[
\boxed{
\begin{array}{ll}
1. & 17.00 \\
2. & 7.07 \\
3. & 10.77 \\
4. & 7.28 \\
5. & 11.66 \\
6. & 16.40 \\
7. & 8.25 \\
8. & 9.43 \\
9. & 5.00 \\
10. & 12.21 \\
\end{array}
}
\]