Question

What is the distance between `(9,-7,1)` and `(3,-5,-2)`?

Answer 1

The distance is `sqrt(49)` or `7`

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)(9))^2 + (color(red)(-5) - color(blue)(-7))^2 + (color(red)(-2) - color(blue)(1))^2)`

`d = sqrt((color(red)(3) - color(blue)(9))^2 + (color(red)(-5) + color(blue)(7))^2 + (color(red)(-2) - color(blue)(1))^2)`

`d = sqrt((-6)^2 + 2^2 + (-3)^2)`

`d = sqrt((36 + 4 + 9)`

`d = sqrt(49) = 7`