How do you find the distance when given two coordinate points?

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Answer 1 · 2014-11-06T16:00:01

Distance Formula

The distance $D$ $D$ between two points $(x_{1}, y_{1})$ $(x_1,y_1)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ can be found by

$D = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $D=sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Example

Find the distance between the points $(1, - 2)$ $(1,-2)$ and $(5, 1)$ $(5,1)$ .

Let $(x_{1}, y_{1}) = (1, - 2)$ $(x_1,y_1)=(1,-2)$ and $(x_{2}, y_{2}) = (5, 1)$ $(x_2,y_2)=(5,1)$ .

By Distance Formula above,

$D = \sqrt{{(5 - 1)}^{2} + {[1 - (- 2)]}^{2}} = \sqrt{16 + 9} = \sqrt{25} = 5$ $D=sqrt{(5-1)^2+[1-(-2)]^2}=sqrt{16+9}=sqrt{25}=5$

I hope that this was helpful.