Question

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

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

`d = sqrt(3^2 + 4^2 + (-4)^2)`

`d = sqrt(9 + 16 + 16)`

`d = sqrt(41) = 6.403` rounded to the nearest thousandth