Question

If the lines $x+y=0,x-y=0$ and $2x+3y-6=0$ are the sides of a triangle and $(-2,a)$ is an interior point of the triangle then a lies.

• A. $2<a<10/3$
• B. $-2<a<10/3$
• C. $-1<a<9/2$
• D. $-3>a>9/2$

Answer 1

The correct option is A $2<a<10/3$

We have plotted the diagram by finding the point of intersections of lines.

Now point $P(-2,a)$ is interior point of triangle $ABC$ only if its above $Q$ and below $R$.

We can find $Q$ and $R$ as they intersect lines $AC$ and $AB$ respectively.

$x=-2$ for both $Q$ and $R$

For $Q$, $x+y=0\Rightarrow y=-x\Rightarrow y=2\Rightarrow a>2$

For $R$, $2x+3y-6=0\Rightarrow y=\frac{6-2x}{3}\Rightarrow y=\frac{10}{3}\Rightarrow a<\frac{10}{3}$

$2<a<\frac{10}{3}$