Points inside the triangle with vertices at ( | vedclass

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Question

(B) Let the vertices be $A(1,3), B(5,0)$,and $C(-1,2)$.For any point $(x,y)$ inside the triangle,the expression must maintain the same sign as it does

Vedclass · Accepted Answer

$3x + 2y > 0$

Vedclass · Answer

(B) Let the vertices be $A(1,3), B(5,0)$,and $C(-1,2)$.For any point $(x,y)$ inside the triangle,the expression must maintain the same sign as it does for the vertices if the line does not pass through the triangle.Testing the expression $3x + 2y$ for the vertices:For $A(1,3): 3(1) + 2(3) = 3 + 6 = 9 > 0$.For $B(5,0): 3(5) + 2(0) = 15 + 0 = 15 > 0$.For $C(-1,2): 3(-1) + 2(2) = -3 + 4 = 1 > 0$.Since the value is positive for all vertices,any point inside the triangle must satisfy $3x + 2y > 0$.Therefore,option $B$ is correct.

Points inside the triangle with vertices at $(1,3), (5,0)$ and $(-1,2)$ must necessarily satisfy which of the following conditions?

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