Question

What is the distance between `(1,-3,2)` and `(5,4,-3)`?

Answer 1

The distance between the two points is `sqrt(90)` or `9.487` rounded to the nearest thousandth.

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)(5) - color(blue)(1))^2 + (color(red)(4) - color(blue)(-3))^2 + (color(red)(-3) - color(blue)(2))^2)`

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

`d = sqrt(4^2 + 7^2 + (-5)^2)`

`d = sqrt(16 + 49 + 25)`

`d = sqrt(90) = 9.487`