Question

What is the distance between `(4,2,2)` and `(5,-3,-1)`?

Answer 1

`d=sqrt(35)`

Explanation:

Imagine a strong light directly above the line such that the z-axis is vertical and the xy-plane is horizontal. The line would cast a shadow onto the xy-plane (Projected image) and it would in all likelihood form a triangle with the x and y axis.

You could use Pythagoras to determine the length of this projection. You could again use Pythagoras to find the true length but this time the z-axis being as if it is the opposite and the projection being the adjacent.

By going through this process you will find that the final equation boils down to:

Let the distance between the points be d

`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)`

`d=sqrt(1^2+(-5)^2+(-3)^2)`

`d=sqrt(35)`