Finding Distance of Two Points

Learn how to find the distance of two points on the coordinate plane by using the distance formula.

Step by step guide to find distance of two points

• Distance of two points A \((x_{1},y_{1})\) and B \((x_{2},y_{2})\)
  \(\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}\)

Example 1:

Find the distance of two points \((1,6) \ and \ (4,2)\).

Solution:

Use distance of two points formula: \(\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}\)
\((x_{1},y_{1})=(1,6)\) and \((x_{2},y_{2})=(4,2)\). Then: →
\(d=\sqrt{4−(1))^{2}+(2−6)^{2}}=\sqrt{(3)^{2}+(−4)^{2}}=\sqrt{9+16}=\sqrt{25}=5→d=5\)

Example 2:

Find the distance of two points \((-1,5) \ and \ (-3,-6)\).

Solution:

Use distance of two points formula: \(\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}\)
\((x_{1},y_{1})=(-1,5)\) and \((x_{2},y_{2})=(-3,-6)\). Then: \(→\)
\(d=\sqrt{-3−(-1))^{2}+(-6−(5))^{2}}=\sqrt{(-2)^{2}+(−11)^{2}}=\sqrt{4+121}=\sqrt{125}=5\sqrt{5}\) Then: \(d=5 \sqrt{5} \)

Example 3:

Find the distance of two points \((0,8) \ and \ (-4,5)\).

Solution:

Use distance of two points formula: \(\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}\)
\( (x_{1},y_{1})=(0,8)\) and \((x_{2},y_{2})=(−4,5)\). Then: \(d=\sqrt{(x_{1}−x_{2})^2+(y_{1}−y_{2})^2}→\)
\(d=\sqrt{(0−(−4))^2+(8−5)^2}=\sqrt{(4)^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5→d=5\)

Example 4:

Find the distance of two points \((4,2) \ and \ (-5,-10)\).

Solution:

Use distance of two points formula: \(\color{blue}{d=\sqrt{(x_2-x_1)^{2}+(y_{2}-y_{1}){^2}}}\)
\( (x_{1},y_{1})=(4,2)\) and \((x_{2},y_{2})=(−5,-10)\). Then: \(d=\sqrt{(x_{1}−x_{2})^2+(y_{1}−y_{2})^2}→\)
\(d=\sqrt{(4−(−5))^2+(2−(-10))^2}=\sqrt{(9)^2+(12)^2}=\sqrt{81+144}=\sqrt{225}=25→d=15\)

Exercises

Find the distance between each pair of points.

1. \(\color{blue}{(2, –1), ( 1, – 1)}\)
2. \(\color{blue}{ (6, 4), (– 2, 10)}\)
3. \(\color{blue}{(– 8, – 5), (– 5, -1)}\)
4. \(\color{blue}{(– 6, – 10), (– 2, – 10)}\)
5. \(\color{blue}{(4, – 6), (9, 6)}\)
6. \(\color{blue}{(– 6, – 7), (2, 8)}\)

Download Finding Distance of Two Points Worksheet

1. \(\color{blue}{1}\)
2. \(\color{blue}{10}\)
3. \(\color{blue}{5}\)
4. \(\color{blue}{4}\)
5. \(\color{blue}{13}\)
6. \(\color{blue}{17}\)