Mathematics

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.


ANSWER

$$2 < a < 10/3$$


SOLUTION
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 $$R$$, $$2x+3y-6=0\Rightarrow y=\dfrac{6-2x}{3} \Rightarrow y=\dfrac{10}{3}\Rightarrow a<\dfrac{10}{3}$$
$$2<a<\dfrac{10}{3}$$
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Single Correct Medium Published on 09th 09, 2020
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