Question

What is the distance between `(3,-29,-12)` and `(2,-38,-6)`?

Answer 1

See a solution process below:

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)(2) - color(blue)(3))^2 + (color(red)(-38) - color(blue)(-29))^2 + (color(red)(-6) - color(blue)(-12))^2)`

`d = sqrt((color(red)(2) - color(blue)(3))^2 + (color(red)(-38) + color(blue)(29))^2 + (color(red)(-6) + color(blue)(12))^2)`

`d = sqrt((-1)^2 + (-9)^2 + 6^2)`

`d = sqrt(1 + 81 + 36)`

`d = sqrt(118)`

Or if a non-radical answer is required:

`d = 10.863` rounded to the nearest thousandth.