Question

What is the distance between `(2,12,5)` and `(-1,7,5)`?

Answer 1

The distance between the two points is `sqrt(34)` or `5.831` rounded to the nearest thousandth.

Explanation:

The formula for calculating the distance between two points is:

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

Substituting the values from the points in the problem gives:

`d = sqrt((color(red)(-1) - color(blue)(2))^2 + (color(red)(7) - color(blue)(12))^2 + (color(red)(5) - color(blue)(5))^2)`

`d = sqrt((-3)^2 + (-5)^2 + 0^2)`

`d = sqrt(9 + 25 + 0)`

`d = sqrt(34) = 5.831` rounded to the nearest thousandth.