Question

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

Answer 1

`10" units"`

Explanation:

using the 3-d version of the `color(blue)"distance formula"`

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

`"the 2 points here are " (-6,3,1)" and " (2,-3,1)`

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

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

`color(white)(d)=sqrt(64+36+0)`

`color(white)(d)=sqrt100=10" units"`