What is the distance between # (–2, 1, 3) # and #(–6, 3, 1) #?

1 Answer
Jim G.
Sep 1, 2016

#2sqrt6#

Explanation:

Using the #color(blue)"3-d version of the distance formula"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2))color(white)(a/a)|)))#
where # (x_1,y_1,z_1)" and " (x_2,y_2,z_2)" are 2 coordinate points."#

Here the 2 points are (-2 ,1 ,3) and (-6 ,3 ,1)

let #(x_1,y_1,z_1)=(-2,1,3)" and " (x_2,y_2,z_2)=(-6,3,1)#

#d=sqrt((-6+2)^2+(3-1)^2+(1-3)^2)#

#=sqrt(16+4+4)=sqrt24==sqrt(4xx6)=2sqrt6#

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