Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.
-$$\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } , \right\}$$
Barycentric coordinates: $\left( \frac { 1 } { 2 } , 0 , \frac { 1 } { 8 } , \frac { 3 } { 8 } \right)$
A) Inside
B) Outside
C) Edge
D) Face

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The Answer of Use the barycentric coordinates with respect to S to determine if the point p is inside, outside, on a face, or on the edge
of conv S which is a tetrahedron.
-$$\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } , \right\}$$
Barycentric coordinates: $\left( \frac { 1 } { 2 } , 0 , \frac { 1 } { 8 } , \frac { 3 } { 8 } \right)$
A) Inside
B) Outside
C) Edge
D) Face

Use the Barycentric Coordinates with Respect to S to Determine S={v1,v2,v3,v4,}\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } , \right\}S={v1​,v2​,v3​,v4​,}

Use the Barycentric Coordinates with Respect to S to Determine $\mathrm { S } = \left\{ \mathbf { v } _ { 1 } , \mathbf { v } _ { 2 } , \mathbf { v } _ { 3 } , \mathbf { v } _ { 4 } , \right\}$