The length of the perpendicular drawn from th | vedclass

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

Question

(B) The equation of the line passing through $(x', y')$ and $(x'', y'')$ is given by: $(y - y') = \frac{y'' - y'}{x'' - x'}(x - x')$ $(y - y')(x'' - x

Vedclass · Accepted Answer

$\frac{|x'y'' - y'x''|}{\sqrt{(x'' - x')^2 + (y'' - y')^2}}$

Vedclass · Answer

(B) The equation of the line passing through $(x', y')$ and $(x'', y'')$ is given by: $(y - y') = \frac{y'' - y'}{x'' - x'}(x - x')$ $(y - y')(x'' - x') = (y'' - y')(x - x')$ $x(y'' - y') - y(x'' - x') + y'x'' - y'x' - x'y'' + x'y' = 0$ $x(y'' - y') - y(x'' - x') + (x'y'' - y'x'') = 0$ The length of the perpendicular from the origin $(0, 0)$ to the line $Ax + By + C = 0$ is $\frac{|C|}{\sqrt{A^2 + B^2}}$. Here,$A = (y'' - y')$,$B = -(x'' - x')$,and $C = (x'y'' - y'x'')$. Thus,the length is $\frac{|x'y'' - y'x''|}{\sqrt{(y'' - y')^2 + (-(x'' - x'))^2}} = \frac{|x'y'' - y'x''|}{\sqrt{(x'' - x')^2 + (y'' - y')^2}}$.

The length of the perpendicular drawn from the origin $(0, 0)$ to the line joining the points $(x', y')$ and $(x'', y'')$ is:

Similar Questions

If $P(\alpha, \beta)$ is a point on the line $3x + y = 0$ such that the point $P$ and the point $Q(1, 1)$ lie on opposite sides of the line $3x - 4y - 8 = 0$,then:

If $p$ is the length of the perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$,then show that $\frac{1}{p^{2}} = \frac{1}{a^{2}} + \frac{1}{b^{2}}$.

Find the equation of the line which is equidistant from the parallel lines $9x + 6y - 7 = 0$ and $3x + 2y + 6 = 0$.

Find the length of the perpendicular drawn from the origin to the line $\sqrt{3}x - y + 2 = 0$.

$A$ line $L_1$ passing through the point of intersection of the lines $x-2y+3=0$ and $2x-y=0$ is parallel to the line $L_2$. If $L_2$ passes through the origin and also through the point of intersection of the lines $3x-y+2=0$ and $x-3y-2=0$,then the distance between the lines $L_1$ and $L_2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module