Question

All points lying inside the triangle formed by the points $(1,3),(5,0)$ and $(-1,2)$ satisfy

• A. $3x+2y\ge 0$
• B. $2x+y\ge 0$
• C. $2x-3y-12\ge 0$
• D. $-2x+y\ge 0$

Answer 1

Answer: (A), (C)

The correct options are
A $3x+2y\ge 0$
C $2x-3y-12\ge 0$

A)Substitute (1,3), (5,0) and (-1,2) in $3x+2y\ge 0$

$3\left(1\right)+2\left(3\right)=9\ge 0$

$3\left(5\right)+2\left(0\right)=15\ge 0$

$3(-1)+2\left(2\right)=1\ge 0$

As (1,3), (5,0) and (-1,2) satisfy $3x+2y\ge 0$

B)Similarly, since (1,3), (5,0) and (-1,2) do not satisfy $2x+y-13\ge 0$

C)Similarly, since (1,3), (5,0) and (-1,2) do not satisfy $2x-3y-12\le 0$

D)Similarly, since (5,0) do not satisfy $-2x+y\ge 0$