Question

What is the distance between `(–2, 1, 3)` and `(0, 4, –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)(0) - color(blue)(-2))^2 + (color(red)(4) - color(blue)(1))^2 + (color(red)(-2) - color(blue)(3))^2)`

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

`d = sqrt(2^2 + 3^2 + (-5)^2)`

`d = sqrt(4 + 9 + 25)`

`d = sqrt(38)`

Or

`d = 6.164` rounded to the nearest thousandth.