How to Find Distance of Two Points? (+FREE Worksheet!)

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Step-by-step guide to finding the distance between 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 For education statistics and research National Center for Education Statistics.

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: →
\(d=\sqrt{(4−1)^{2}+(2−6)^{2}}=\sqrt{(3)^{2}+(−4)^{2}}=\sqrt{9+16}=\sqrt{25}=5→d=5\)

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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: \(→\)
\(d=\sqrt{(-3−(-1))^{2}+(-6−5)^{2}}=\sqrt{(-2)^{2}+(−11)^{2}}=\sqrt{4+121}=\sqrt{125}=5\sqrt{5}\) → \(d=5 \sqrt{5} \)

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:→
\(d=\sqrt{(−4−0)^2+(5−8)^2}=\sqrt{(-4)^2+(-3)^2}=\sqrt{16+9}=\sqrt{25}=5→d=5\)

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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: →
\(d=\sqrt{( − 5−4)^2+(−10-2)^2}=\sqrt{(-9)^2+(-12)^2}=\sqrt{81+144}=\sqrt{225}=15→d=15\)

Exercises for Finding Distance of Two Points

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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