Question

What is the distance between `(5, –6, 4)` and `(–1, 1, 3)`?

Answer 1

The distance between the two points is `sqrt(86)` or `9.274` 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(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)(5))^2 + (color(red)(1) - color(blue)(-6))^2 + (color(red)(3) - color(blue)(4))^2)`

`d = sqrt((color(red)(-1) - color(blue)(5))^2 + (color(red)(1) + color(blue)(6))^2 + (color(red)(3) - color(blue)(4))^2)`

`d = sqrt((-6)^2 + 7^2 + (-1)^2)`

`d = sqrt(36 + 49 + 1)`

`d = sqrt(86) = 9.274` rounded to the nearest hundredth