One can define the cartesian coordinates of a random point C in the plane relatively to two given points A and B. One can define C also ralatively to Point Vectors [math]\vec{A}[/math] en [math]\vec{B}[/math]. [br]The lines AB, OA en OB devide the plane into 7 regions. Explore how these line define the sign and/or size of the barycentric coordinates
The line AB defines the size of the coordinates:[br]- For points on the line the sum of the coordinates equals 1.[br]- For points in the semi-plane of the origin the sum < 1.[br]- For points on the other side of the line of the origin the sum > 1.[br]The line OB defines the sign of the first coordinate number (= relative to [math]\vec{A}[/math]):[br]- For points on the same side as A it's positive.[br]- For points on the line it equals 0.[br]- For points on the othes side tha A it's negative.[br]The line OA defines the sign of the second coordinate number (= relative to [math]\vec{B}[/math]):[br]- For points on the same side as B it's positive.[br]- For points on the line it equals 0.[br]- For points on the othes side tha B it's negative.[br][br]