Question

What is the distance between `(3, –1, 1)` and `(1, –2, 0)`?

Answer 1

`sqrt6~~2.45" to 2 dec. places"`

Explanation:

Use 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 " (3,-1,1)" and " (1,-2,0)`

`"let " (x_1,y_1,z_1)=(3,-1,1),(x_2,y_2,z_2)=(1,-2,0)`

`d=sqrt((1-3)^2+(-2+1)^2+(0-1)^2)`

`color(white)(d)=sqrt(4+1+1)`

`color(white)(d)=sqrt6~~2.45" to 2 dec. places"`