Question

What is the distance between `(1,-10,-3)` and `(4,3,-2)`?

Answer 1

The distance between the points is `sqrt(179)` or `13.379` 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)(4) - color(blue)(1))^2 + (color(red)(3) - color(blue)(-10))^2 + (color(red)(-2) - color(blue)(-3))^2)`

`d = sqrt((color(red)(4) - color(blue)(1))^2 + (color(red)(3) + color(blue)(10))^2 + (color(red)(-2) + color(blue)(3))^2)`

`d = sqrt(3^2 + 13^2 + 1^2)`

`d = sqrt(9 + 169 + 1)`

`d = sqrt(179) = 13.379`