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.
- \(\color{blue}{(2, –1), ( 1, – 1)}\)
- \(\color{blue}{ (6, 4), (– 2, 10)}\)
- \(\color{blue}{(– 8, – 5), (– 5, -1)}\)
- \(\color{blue}{(– 6, – 10), (– 2, – 10)}\)
- \(\color{blue}{(4, – 6), (9, 6)}\)
- \(\color{blue}{(– 6, – 7), (2, 8)}\)
Download Finding Distance of Two Points Worksheet
- \(\color{blue}{1}\)
- \(\color{blue}{10}\)
- \(\color{blue}{5}\)
- \(\color{blue}{4}\)
- \(\color{blue}{13}\)
- \(\color{blue}{17}\)
