# Linear combinations of vectors using a triangle

- Author:
- Lin Loi

- Topic:
- Vectors

A point is outside a triangle if one of the lambda values is smaller than 0

Points A,B,C are the vertices of the triangle. Point D is the point to check if it is inside the triangle ABC.
Form vectors AB and AC and we are solving for the system of equations with 2 unknowns and 2 equations, which means that there have to be exactly one solution to the unknowns.
The equation:
lamda1*AB + lambda2*AC = AD
when separation the above equation, we get one equation expressed with all the x-coordinates of all points and another equation expressed with all the y-coordinates of all points.
Note that the lambda values are not barycentric coordinates but a linear combination of the edge-vectors