Question

What is the distance between `(–1, 1, 3)` and `(–5, –1, 1)`?

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)(-5) - color(blue)(-1))^2 + (color(red)(-1) - color(blue)(1))^2 + (color(red)(1) - color(blue)(3))^2)`

`d = sqrt((color(red)(-5) + color(blue)(1))^2 + (color(red)(-1) - color(blue)(1))^2 + (color(red)(1) - color(blue)(3))^2)`

`d = sqrt((-4)^2 + (-2)^2 + (-2)^2)`

`d = sqrt(16 + 4 + 4)`

`d = sqrt(24)`

`d = sqrt(4 * 6)`

`d = sqrt(4)sqrt(6)`

`d = 2sqrt(6)`

Or, if you require a non-radical answer:

`d = 4.899` rounded to the nearest thousandth