The lines $L_1: y-x=0$ and $L_2: 2 x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$ respectively. The…

The lines $L_1: y-x=0$ and $L_2: 2 x+y=0$ intersect the line $L_3: y+2=0$ at $P$ and $Q$ respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersect $L_3$ at $R$. This question has Statement $-1$ and Statement $-2$. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : The ratio $P R: R Q$ equals $2 \sqrt{2}: \sqrt{5}$. Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.
  1. Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is not a correct explanation for Statement $-1$
  2. Statement $-1$ is true, Statement- 2 is false.
  3. Statement $-1$ is false, Statement- 2 is true.
  4. Statement $-1$ is true, Statement $-2$ is true; Statement $-2$ is a correct explanation for Statement $-1$

Solution


$ P(-2,-2) ; Q=(1,-2) $ Equation of angular bisector $\overline{\mathrm{OR}}$ is $(\sqrt{5}+2 \sqrt{2}) \mathrm{x}=(\sqrt{5}-\sqrt{2}) \mathrm{y}$ $ \therefore P R: R Q=2 \sqrt{2}: \sqrt{5} $

Asked in: JEE Main 2011

Practice more Straight Lines questions on Aicharya