The orthocentre of the triangle formed by lin | vedclass

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

Question

(A) Given lines are:$L_1: x+y+1=0$$L_2: x-y-1=0$$L_3: 3x+4y+5=0$Slope of $L_1$ $(m_1)$ is $-1$.Slope of $L_2$ $(m_2)$ is $1$.Since $m_1 	imes m_2 = (

Vedclass · Accepted Answer

$(0,-1)$

Vedclass · Answer

(A) Given lines are:$L_1: x+y+1=0$$L_2: x-y-1=0$$L_3: 3x+4y+5=0$Slope of $L_1$ $(m_1)$ is $-1$.Slope of $L_2$ $(m_2)$ is $1$.Since $m_1 	imes m_2 = (-1) 	imes (1) = -1$,the lines $L_1$ and $L_2$ are perpendicular to each other.Therefore,the triangle is a right-angled triangle,and the orthocentre of a right-angled triangle is the vertex where the right angle is formed.To find the vertex,solve $L_1$ and $L_2$:$x+y+1=0$$x-y-1=0$Adding the two equations: $2x = 0 \Rightarrow x = 0$.Substituting $x=0$ in $x+y+1=0$,we get $0+y+1=0 \Rightarrow y = -1$.Thus,the orthocentre is $(0, -1)$.

The orthocentre of the triangle formed by lines $x+y+1=0$,$x-y-1=0$,and $3x+4y+5=0$ is

Similar Questions

The centroid of a triangle,whose vertices are $(2, 1)$,$(5, 2)$,and $(3, 4)$,is

What is the distance from the origin to the centroid of the triangle formed by the points $(1, 1)$,$(0, -7)$,and $(-4, 0)$?

What is the distance of the orthocenter from the vertex of a triangle with vertices $(2, 3), (4, 5),$ and $(-1, 10)$?

If the vertices $P, Q, R$ of a triangle $PQR$ are rational points,which of the following points of the triangle $PQR$ is (are) always a rational point $(s)$? ($A$ rational point is a point both of whose coordinates are rational numbers.)

Two vertices of a triangle are $(5, -1)$ and $(-2, 3)$. If the orthocentre is the origin,then the coordinates of the third vertex are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module