Question

What is the distance between `(6, 0, 4)` 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)(6))^2 + (color(red)(4) - color(blue)(0))^2 + (color(red)(-2) - color(blue)(4))^2)`

`d = sqrt((-7)^2 + 4^2 + (-6)^2)`

`d = sqrt(49 + 16 + 36)`

`d = sqrt(101)`

or

`d ~= 10.05`