Question

What is the distance between `(3, –1, 1)` and `(6, 0, 4)`?

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)(6) - color(blue)(3))^2 + (color(red)(0) - color(blue)(-1))^2 + (color(red)(4) - color(blue)(1))^2)`

`d = sqrt((color(red)(6) - color(blue)(3))^2 + (color(red)(0) + color(blue)(1))^2 + (color(red)(4) - color(blue)(1))^2)`

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

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

`d = sqrt(19)`

Or

`d = 4.359` rounded to the nearest thousandth.