Question

What is the distance between `(-13,13,-4)` and `(-1,-6,-2)`?

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)(-1) - color(blue)(-13))^2 + (color(red)(-6) - color(blue)(13))^2 + (color(red)(-2) - color(blue)(-4))^2)`

`d = sqrt((color(red)(-1) + color(blue)(13))^2 + (color(red)(-6) - color(blue)(13))^2 + (color(red)(-2) + color(blue)(4))^2)`

`d = sqrt(12^2 + (-19)^2 + 2^2)`

`d = sqrt(144 + 361 + 4)`

`d = sqrt(509)`

Or

`d = 22.561` rounded to the nearest thousandth