(A) The equations of the sides are given as:$AB: x-3y=0$$AC: 3x-y=0$$BC: x+y+4=0$To find the coordinates of vertex $B$,we solve the equations of lines

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(A) The equations of the sides are given as:$AB: x-3y=0$$AC: 3x-y=0$$BC: x+y+4=0$To find the coordinates of vertex $B$,we solve the equations of lines $AB$ and $BC$:$x-3y=0 \Rightarrow x=3y$Substitute $x=3y$ into $x+y+4=0$:$3y+y+4=0$ $\Rightarrow 4y=-4$ $\Rightarrow y=-1$Then $x=3(-1)=-3$.So,the vertex $B$ is $(-3, -1)$.Since the line $3x-y+k=0$ passes through $B(-3, -1)$,we substitute these coordinates into the line equation:$3(-3)-(-1)+k=0$$-9+1+k=0$$-8+k=0 \Rightarrow k=8$.

Class 11 Mathematics Straight Lines Slope of line, Equation of line in different forms

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The equations of the sides $AB$,$AC$,and $BC$ of a $\triangle ABC$ are respectively $x-3y=0$,$3x-y=0$,and $x+y+4=0$. If $P$ and $Q$ are points on the line $3x-y+k=0$ passing through $B$ such that $PB:BQ=1:1$,then $k=$

TS EAMCET 2020 All TS EAMCET

A
$8$
B
$12$
C
$-8$
D
$-12$

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Straight Lines

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Slope of line, Equation of line in different forms

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The equations of the sides $AB$,$AC$,and $BC$ of a $\triangle ABC$ are respectively $x-3y=0$,$3x-y=0$,and $x+y+4=0$. If $P$ and $Q$ are points on the line $3x-y+k=0$ passing through $B$ such that $PB:BQ=1:1$,then $k=$

Similar Questions

If the straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive direction of $X$-axis and meets the line $12x + 5y + 10 = 0$ at $Q$,then the length of $PQ$ is

Consider the following population and year graph (Fig.),find the slope of the line $AB$ and using it,find what will be the population in the year $2010$?

The equation of a line passing through the intersection of lines $x = 0$ and $y = 0$ and through the point $(2, 2)$ is:

The angles made with the $X$-axis by the two lines passing through the point $P(1, 2)$ and cutting the line $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ units from the point $P$ are

In what direction should a line be drawn through the point $(1, 2)$ so that its point of intersection with the line $x + y = 4$ is at a distance of $\frac{\sqrt{6}}{3}$ from the given point (in $^\circ$)?

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