Scrub the values of A and B coordinates to see how they connect to terms in the final distance formula. Now imagine two points lets say they are 00 and 34 to keep it simple. Join the points by a line and it forms a line segment P Q.
Join the points by a line and it forms a line segment P Q.
To derive the distance between two points A and B we imagine a third point C that forms a right triangle and then use the Pythagorean Theorem. Two of the right triangles have been drawn. Proof of the Perpendicular Distance Formula Lets start with the line Ax By C 0 and label it DE. Given two points you can always plot them draw the right triangle and then find the length of the hypotenuse.