Question

What is the distance between `(–2, 1, 3)` and `(3, –1, 1)`?

Answer 1

The distance between the two points is `sqrt(33)` or `5.745` 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)(3) - color(blue)(-2))^2 + (color(red)(-1) - color(blue)(1))^2 + (color(red)(1) - color(blue)(3))^2)`

`d = sqrt((color(red)(3) + color(blue)(2))^2 + (color(red)(-1) - color(blue)(1))^2 + (color(red)(1) - color(blue)(3))^2)`

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

`d = sqrt(25 + 4 + 4)`

`d = sqrt(33) = 5.745` rounded to the nearest thousandth.