Question

What is the distance between `(8,-4,6)` and `(-1,-3,5)`?

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)(8))^2 + (color(red)(-3) - color(blue)(-4))^2 + (color(red)(5) - color(blue)(6))^2)`

`d = sqrt((color(red)(-1) - color(blue)(8))^2 + (color(red)(-3) + color(blue)(4))^2 + (color(red)(5) - color(blue)(6))^2)`

`d = sqrt(-9^2 + 1^2 + (-1)^2)`

`d = sqrt(81+ 1 + 1)`

`d = sqrt(83)`

Or

`d = 9.110` rounded to the nearest thousandth.