How to Find Distance of Two Points

How to Find Distance of Two Points

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

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Step by step guide to find the distance of two points

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

Finding Distance of Two Points – 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: →
\(d=\sqrt{4−(1))^{2}+(2−6)^{2}}=\sqrt{(3)^{2}+(−4)^{2}}=\sqrt{9+16}=\sqrt{25}=5→d=5\)

Finding Distance of Two Points – 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: \(d=5 \sqrt{5} \)

Finding Distance of Two Points – 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: \(d=\sqrt{(x_{1}−x_{2})^2+(y_{1}−y_{2})^2}→\)
\(d=\sqrt{(0−(−4))^2+(8−5)^2}=\sqrt{(4)^2+(3)^2}=\sqrt{16+9}=\sqrt{25}=5→d=5\)

Finding Distance of Two Points – 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 for Finding Distance of Two Points

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. \(\color{blue}{17}\)

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