Question

What is the distance between `(13,23,-10)` and `(-3,17,-22)`?

Answer 1

See the entire 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)(-3) - color(blue)(13))^2 + (color(red)(17) - color(blue)(23))^2 + (color(red)(-22) - color(blue)(-10))^2)`

`d = sqrt((color(red)(-3) - color(blue)(13))^2 + (color(red)(17) - color(blue)(23))^2 + (color(red)(-22) + color(blue)(10))^2)`

`d = sqrt((-16)^2 + (-6)^2 + (-12)^2)`

`d = sqrt(256 + 36 + 144)`

`d = sqrt(436) = 20.881` rounded to the nearest thousandth.