Add one more axis to a plane, and you can locate all of space with coordinates
Move a point's position with the x, y, and z sliders, and check the distance from the origin — and the distance between two points — directly with the formula.
A point on a plane can be located with just two numbers, (x, y), but the world we live in is three-dimensional. To describe a drone's position in a room, you need more than "left/right, forward/back" — you also need "how high off the floor," so a third number, z, gets added, giving (x, y, z).
To find the distance from the origin to a point P, the Pythagorean theorem gets used twice. First find the length of the diagonal along the floor, then build a second right triangle out of that diagonal and the height z, and you get √(x²+y²+z²).
Move the point freely with the x, y, and z sliders to check the distance to the origin, and verify the distance formula between two points for yourself too.
Space coordinates — a plane locates position with two numbers (x,y), but space needs a third, an added z-axis, giving three numbers (x,y,z). Think of point P as a corner of a box — the distance from the origin to P is exactly that box's diagonal length.
x2
y3
z2
Distance from origin O(0,0,0) to P = √(x²+y²+z²)
Distance between two points — point A is fixed as the reference point; move point B with the sliders. The distance between two points is the square root of the sum of the squared differences along each coordinate axis. It's exactly the plane distance formula you learned before, with one z-axis term added.