Question

The distance between the points A ( 1 -1 3) B ( 2 3 -5)

Answer 1

Step-by-step explanation:

BY THE DISTANCE FORMULA, WE HAVE

AB =

$\sqrt{ {(x2 - x1) + (y2 - y1)}^{2} }$

AB =

$\sqrt{ {(23 - 1)}^{2} + {( - 5 - 13)}^{2} }$

$\sqrt{ {(22)}^{2} + { ( - 18)}^{2} }$

$\sqrt{484 + 324}$

$\sqrt{808}$

$28.42 \: units$

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Answer 2

Step-by-step explanation:

The distance between two distinct points whose coordinates are

$(x_{1}, y_{1} , z_{1} ) \: \: \: and \: \: ( x_{2} , y_{2} , z_{2})$

is

$AB \: = \sqrt{ {( x_{2} }- x_{1} )^{2} + (y_{2} - y_{1} )^{2} + {( z_{2} - z_{1} })^{2} }$

where

$x_{1} = 1 \: \: \: \: \: \: x_{2} = 2\\ y_{1} = - 1 \: \: \: \: \: y_2 = 3 \\ z_{1} = 3 \: \: \: \: z_{2} = - 5$

Now put this values in the given formula.

$AB \: = \sqrt{( {2 - 1)}^{2} + {(3 + 1)}^{2} + {( - 5 - 3)}^{2} } \\ \\ =>\sqrt{ {(1)}^{2} + {(4)}^{2} + {( - 8)}^{2} } \\ \\ =>\sqrt{1 + 16 + 64} \\ \\ =>\sqrt{17 + 64} \\ \\ =>\sqrt{81} \\ \\ =>9$