# Finding all coordinates of a triangle on a graph using three vertices.

I'm working on computer program and I need to know how to find all of the coordinates (x, y) of a triangle given on a graph using the three vertices. The Triangle may be any type including right, equilateral, obtuse, acute, etc.. Is there any way to find all of these coordinates? Please help.

Let your vertices be $(x_1,y_1)$, $(x_2,y_2)$ and $(x_3,y_3)$
If you only wants the borders, your triangle is : $$\bigcup\limits_{i \ne j, (i,j)\in[1,3]^2}\{(tx_i+(1-t)x_j,ty_i+(1-t)y_j), t \in [0,1])\}$$
else it is : $$\{(\alpha x_1 + \beta x_2 + \gamma x_3,\alpha y_1 + \beta y_2 + \gamma y_3), (\alpha, \beta, \gamma) \in [0,1]^3, \alpha+\beta+\gamma=1\}$$