Question

What is the distance between `(10,5,-2)` and `(12,11,5)`?

Answer 1

See the 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)(12) - color(blue)(10))^2 + (color(red)(11) - color(blue)(5))^2 + (color(red)(5) - color(blue)(-2))^2)`

`d = sqrt((color(red)(12) - color(blue)(10))^2 + (color(red)(11) - color(blue)(5))^2 + (color(red)(5) + color(blue)(2))^2)`

`d = sqrt(2^2 + 6^2 + 7^2)`

`d = sqrt(4 + 36 + 49)`

`d = sqrt(89) = 9.434` rounded to the nearest thousandth.