What is the distance between $(- 10, 6)$ $(-10, 6)$ and $(5, 2)$ $(5, 2)$ ?

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What is the distance between $(- 10, 6)$ $(-10, 6)$ and $(5, 2)$ $(5, 2)$ ?

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Answer 1 · 2016-01-24T17:11:13

The distance formula for Cartesian coordinates is

$d = \sqrt{{(x_{2} - x_{1})}_{2}^{2} + {(y_{2} - y_{1})}_{2}^{2}}$ $d=sqrt((x_2-x_1)^2+(y_2-y_1)^2$
Where $x_{1}, y_{1}$ $x_1, y_1$ , and $x_{2}, y_{2}$ $x_2, y_2$ are the Cartesian coordinates of two points respectively.
Let $(x_{1}, y_{1})$ $(x_1,y_1)$ represent $(- 10, 6)$ $(-10,6)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ represent $(5.2)$ $(5.2)$ .
$\Rightarrow d = \sqrt{{(5 - (- 10))}^{2} + {(2 - 6)}^{2}}$ $implies d=sqrt((5-(-10))^2+(2-6)^2$
$\Rightarrow d = \sqrt{{(5 + 10)}^{2} + {(2 - 6)}^{2}}$ $implies d=sqrt((5+10)^2+(2-6)^2$
$\Rightarrow d = \sqrt{{(15)}^{2} + {(- 4)}^{2}}$ $implies d=sqrt((15)^2+(-4)^2$
$\Rightarrow d = \sqrt{225 + 16}$ $implies d=sqrt(225+16$
$\Rightarrow d = \sqrt{241}$ $implies d=sqrt(241$

Hence the distance between the given points is $\sqrt{241}$ $sqrt(241)$ units.

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What is the distance between $(- 10, 6)$ $(-10, 6)$ and $(5, 2)$ $(5, 2)$ ?

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