Values of $\alpha$ if $(\alpha, 2 \alpha)$ lies inside the $\Delta A B C$ if $A(0,2), B(2,0)$ and $C(4,4)$

$\alpha \in\left(\frac{1}{3}, \frac{2}{3}\right)$

$\alpha \in\left(\frac{2}{3}, 1\right)$

$\alpha \in\left(\frac{1}{3}, 1\right)$

JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

1 Medium

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Application +4 | -1

Values of

\alpha

(\alpha, 2 \alpha)

lies inside the

\Delta A B C

A(0,2), B(2,0)

and

C(4,4)

View answer and explanation

Correct option: C

\alpha \in\left(\frac{2}{3}, \frac{4}{3}\right)

Option C (

\alpha \in\left(\frac{{2}}{{3}}, \frac{{4}}{{3}}\right)

) is correct because the point

(\alpha, 2\alpha)

must satisfy the inequalities derived from the equations of the lines forming the triangle.