Lines L_1: y - x = 0 and L_2: 2x + y = 0 inte | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) For $L_1: y = x$ and $L_3: y = -2$,the intersection point $P$ is $(-2, -2)$.For $L_2: y = -2x$ and $L_3: y = -2$,the intersection point $Q$ is $(1

Vedclass · Accepted Answer

Statement-$1$ and Statement-$2$ are both true and Statement-$2$ is the correct explanation of Statement-$1$.

Vedclass · Answer

(A) For $L_1: y = x$ and $L_3: y = -2$,the intersection point $P$ is $(-2, -2)$.For $L_2: y = -2x$ and $L_3: y = -2$,the intersection point $Q$ is $(1, -2)$.The distance $PQ = |1 - (-2)| = 3$.The angle bisector theorem states that the bisector of an angle of a triangle divides the opposite side into segments proportional to the other two sides.Let $O$ be the origin $(0,0)$. The lengths of the sides are $OP = \sqrt{(-2)^2 + (-2)^2} = 2\sqrt{2}$ and $OQ = \sqrt{1^2 + (-2)^2} = \sqrt{5}$.The bisector of $\angle POQ$ divides $PQ$ in the ratio $OP:OQ = 2\sqrt{2} : \sqrt{5}$.Thus,$PR:RQ = 2\sqrt{2} : \sqrt{5}$.Statement-$1$ is true.Statement-$2$ is the Angle Bisector Theorem,which is a standard geometric property,and it is the correct explanation for the ratio calculation in Statement-$1$.

Similar Questions

The equation of the bisector of the acute angle between the lines $3x - 4y + 7 = 0$ and $12x + 5y - 2 = 0$ is

Let distinct lines $L_1$ and $L_2$ belong to the family of lines $(x - 2y - 3) + \lambda (x + 3y + 2) = 0$. If $B_1$ is the angle bisector of $L_1$ and $L_2$ which passes through the point $A(2, 3)$,then the equation of the other bisector of $L_1$ and $L_2$ is ($\lambda$ is a parameter).

The locus of the points which are at an equal distance from $3x + 4y - 11 = 0$ and $12x + 5y + 2 = 0$ and which is near the origin is:

In a $\triangle ABC$,suppose $y=x$ is the equation of the angle bisector of $\angle B$ and the equation of the side $AC$ is $2x-y=2$. If $2AB=BC$ and the points $A$ and $B$ are $(4,6)$ and $(\alpha, \beta)$ respectively,then $\alpha+2\beta$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module