Straight Lines Question 6
Question 6 - 2024 (29 Jan Shift 1)
In a $\triangle A B C$, suppose $y=x$ is the equation of the bisector of the angle $\mathrm{B}$ and the equation of the side $A C$ is $2 x-y=2$. If $2 A B=B C$ and the point $A$ and $\mathrm{B}$ are respectively $(4,6)$ and $(\alpha, \beta)$, then $\alpha+2 \beta$ is equal to
(1) 42
(2) 39
(3) 48
(4) 45
Show Answer
Answer (1)
Solution
$\mathrm{AD}: \mathrm{DC}=1: 2$
$\frac{4-\alpha}{6-\alpha}=\frac{10}{8}$
$\alpha=\beta$
$\alpha=14$ and $\beta=14$
