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

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Answer 1 · 2018-04-15T19:25:28

$\Rightarrow d = 3 \sqrt{2}$ $=> d = 3sqrt(2)$

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

We are given:

$\Rightarrow (x_{1}, y_{1}) = (2, 5)$ $=> (x_1, y_1) = (2,5)$
$\Rightarrow (x_{2}, y_{2}) = (5, 2)$ $=> (x_2, y_2) = (5,2)$

Hence,

$d = \sqrt{{(2 - 5)}^{2} + {(5 - 2)}^{2}}$ $d = sqrt((2-5)^2+(5-2)^2)$

$\Rightarrow d = \sqrt{{(- 3)}^{2} + {(3)}^{2}}$ $=> d=sqrt((-3)^2+(3)^2)$

$\Rightarrow d = \sqrt{9 + 9}$ $=>d = sqrt(9+9)$

$\Rightarrow d = \sqrt{18}$ $=> d = sqrt(18)$

$\Rightarrow d = \sqrt{9 \cdot 2}$ $=>d = sqrt(9*2)$

$\Rightarrow d = 3 \sqrt{2}$ $=> color(green)(d = 3sqrt(2))$

What is the distance between (2,5) (2,5)(2,5) and (5, 2)(5,2)(5, 2)?