Question

The horizontal distance between two points.

Answer 1

We use the Pythagoras Theorem  to derive a formula for finding the distance between two points in 2- and 3- dimensional space.

Let 

P = (x 1, y 1) 

Q = (x 2, y 2)

be two points on the Cartesian plane

Then from the Pythagoras Theorem we find that the distance between P and Q is

        PQ=((x2-x1)^2+(y2-y1)^2)^0.5          

In a similar way

it can be proved that if 

P = (x 1, y 1, z1) and 

Q = (x 2, y 2, z2) are two points in the 3-dimensional space,

the distance between P and Q is

 PQ=((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)^0.5