Distance Formula in the Complex Plane The difference between the points ab and s tin the complex plane is dsa2tb2. You know that the distance A B between two points in a plane with Cartesian coordinates A x 1 y 1 and B x 2 y 2 is given by the following formula. It can be found starting with a change of variables that moves the origin to coincide with the given point then finding the point on the shifted plane a x b y c z d displaystyle axbyczd that is closest to the origin.
The distance is 0.
Derived from the Pythagorean Theorem the distance formula is used to find the distance between two points in the plane. The distance from a point to a plane is equal to length of the perpendicular lowered from a point on a plane. D x 2 x 1 2 y 2 y 1 2. It can be found starting with a change of variables that moves the origin to coincide with the given point then finding the point on the shifted plane a x b y c z d displaystyle axbyczd that is closest to the origin.