Question

What is the distance between `(3,9,8)` and `(5,8,8)`?

Answer 1

`color(red)("distance" = sqrt5)` or `color(red)(~~2.236)` (rounded to thousandth's place)

Explanation:

The distance between three dimensions is similar to the distance between two dimensions.

We use the formula:
`quadcolor(red)(d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2))`, where `x`, `y`, and `z` are the coordinates.

Let's plug in the values for the coordinates into the formula. Pay attention to the negative signs:
`quadd = sqrt((5-3)^2 + (8-9)^2 + (8-8)^2)`

And now simplify:
`quadd = sqrt((2)^2 + (-1)^2 + (0)^2)`

`quadd = sqrt(4+1)`

`quadcolor(red)(d = sqrt5)` or `color(red)(~~2.236)` (rounded to thousandth's place)

Hope this helps!