barycentric coordinates:
 $ \alpha $ $ \beta $ $ \gamma $ $ \sum $
areas:
 $ \textbf{A}_\alpha $ $ \textbf{A}_\beta $ $ \textbf{A}_\gamma $ $ \sum $ 0
X
Y
a
0
0
b
0
0
c
0
0
p
0
0

Which statement is true? The sum of $\alpha$, $\beta$ and $\gamma$ is always ...

$= 1$
$< 1$
$> 1$
$= 1/\sqrt{2}$
$< 1/\sqrt{2}$
$> 1/\sqrt{2}$

A point is inside the triangle $ \mathbf a $, $ \mathbf b$, $ \mathbf c$ if ...

$\alpha, \beta, \gamma > 0$
$\sum{\alpha, \beta, \gamma} < 1$
$\alpha, \beta, \gamma < 0$
$A_\alpha, A_\beta, A_\gamma > 0$

A barycentric coordinate system is...

an orthogonal coordinate system
an non-orthogonal coordinate system

A point is on the line between $\mathbf a $ and $\mathbf b$ if...

$\alpha = 0$
$\beta = 0$
$\gamma = 0$
$\alpha > 0$
$\beta > 0$
$\gamma > 0$

A point is exactly on $ \mathbf a$ if ...

$\alpha = 0$
$\beta = 0$
$\gamma = 0$

What are the x,y coordinates of a point in the following coordinate system?
$a = \left(\begin {array} {c} -1\\-1\\ \end{array}\right), \alpha = 0.25$
$b = \left(\begin {array} {c} 1\\-1\\ \end{array}\right), \beta = 0.25$
$c = \left(\begin {array} {c} 0\\1\\ \end{array}\right), \gamma = 0.5$
Separate the x and y coordinates with a comma (,) e.g.: 0.5,1.0