Question

What is the distance between `(9, 2, 0)` and `(0, 6, 0)`?

Answer 1

`sqrt97≈9.849`

Explanation:

Use 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 (9 ,2 ,0) and (0 ,6 ,0)

let `(x_1,y_1,z_1)=(9,2,0)" and " (x_2,y_2,z_2)=(0,6,0)`

`d=sqrt((0-9)^2+(6-2)^2+0^2)=sqrt(81+16)=sqrt97≈9.849`

Answer 2

`sqrt(97)`

Explanation:

The (Euclidean) distance between `(x_1, y_1, z_1)` and `(x_2, y_2, z_2)` is given by the distance formula:

`d = sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2`

In our example, `(x_1, y_1, z_1) = (9, 2, 0)`, `(x_2, y_2, z_2) = (0, 6, 0)` and we find:

`d = sqrt((0-9)^2+(6-2)^2+(0-0)^2) = sqrt(81+16+0) = sqrt(97)`