Question

What is the distance between `(-7,-6,4)` and `(-2,3,4)`?

Answer 1

See a 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)(-2) - color(blue)(-7))^2 + (color(red)(3) - color(blue)(-6))^2 + (color(red)(4) - color(blue)(4))^2)`

`d = sqrt((color(red)(-2) + color(blue)(7))^2 + (color(red)(3) + color(blue)(6))^2 + (color(red)(4) - color(blue)(4))^2)`

`d = sqrt(5^2 + 9^2 + 0^2)`

`d = sqrt(25 + 81 + 0)`

`d = sqrt(106)`

Or, if you need a single number:

`d = 10.296` rounded to the nearest thousandth