What is the distance between $(10, 8)$ $(10, 8)$ and $(- 10, 6)$ $(-10, 6)$ ?

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What is the distance between $(10, 8)$ $(10, 8)$ and $(- 10, 6)$ $(-10, 6)$ ?

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Answer 1 · 2016-01-21T00:21:10

$2 \sqrt{101}$ $2sqrt(101$

Explanation:

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 $(10, 8)$ $(10,8)$ and $(x_{2}, y_{2})$ $(x_2,y_2)$ represent $(- 10.6)$ $(-10.6)$ .
$\Rightarrow d = \sqrt{{(- 10 - 10)}^{2} + {(6 - 8)}^{2}}$ $implies d=sqrt((-10-10)^2+(6-8)^2$
$\Rightarrow d = \sqrt{{(- 20)}^{2} + {(- 2)}^{2}}$ $implies d=sqrt((-20)^2+(-2)^2$
$\Rightarrow d = \sqrt{400 + 4}$ $implies d=sqrt(400+4$
$\Rightarrow d = 2 \sqrt{100 + 1}$ $implies d=2sqrt(100+1$
$\Rightarrow d = 2 \sqrt{101}$ $implies d=2sqrt(101$

Hence the distance between the given points is $2 \sqrt{101}$ $2sqrt(101)$ units.

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What is the distance between $(10, 8)$ $(10, 8)$ and $(- 10, 6)$ $(-10, 6)$ ?

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