Question

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

Answer 1

The distance between the points is `sqrt(11)` or `3.317` 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)(2) - color(blue)(1))^2 + (color(red)(-3) - color(blue)(3))^2)`

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

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

`d = sqrt(1 + 1 + 9)`

`d = sqrt(11) = 3.317` rounded to the nearest thousandth.