Question

What is the distance between `(–1, 1, 3)` and `(4, –1, 2)`?

Answer 1

The distance is `sqrt(30)` or `5.48` rounded to the nearest hundredth

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(green)(z_2) - color(green)(z_1))^2)`

Substituting the values from the problem gives:

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

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

`d = sqrt(5^2 + (-2)^2 + (-1)^2)`

`d = sqrt(25 + 4 + 1)`

`d = sqrt(30) = 5.48` rounded to the nearest hundredth