Question

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

• A. $3x+2y\ge 0$
• B. $2x+y-13\ge 0$
• C. $2x-3y-15\le 0$
• D. $2x-y\le 0$

Answer 1

Answer: (A), (C)

The correct options are
A $3x+2y\ge 0$
C $2x-3y-15\le 0$

If all the three vertices of a triangle lie on one side of a line, all the interior points of that triangle lie on the same side of that line.

Substituting the coordinates value $(1,3),(5,0)$and $(-1,2)$ in$3x+2y$, we get $9,15,1$ which are all positive.

$\therefore$ All the points lying inside the triangle formed by given points satisfy $3x+2y\ge 0$
Similarly, all the points lying inside the triangle also satisfy $2x-3y-15\le 0$