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.

$2 < a < 10/3$

##### 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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