Question

The length of perpendicular drawn from origin on the line joining (x' , y') and (x" , y") is :

Answer 1

Given : line joining (x' , y') and (x" , y")

To Find :  Length of perpendicular drawn from  origin on line

Solution:

Standard form of straight line ax+by+c=0,

perpendicular shortest distance from point (x , y)  to line is given by

  | (ax + by + c )/ √(a² + b² ) |

line joining (x' , y') and (x" , y")  

y -  y' = { ( y" - y')/(x'' - x') } (x - x')

=> (y -  y')(x'' - x') =  ( y" - y')(x - x')

=> y(x'' - x')  - y'x'' + y'x'  = x ( y" - y') - x'y'' + x'y'

=> y(x'' - x')  - y'x''   = x ( y" - y') - x'y''  

=>  x ( y" - y') -  y(x'' - x')  + y'x'' - x'y''  = 0

=> x ( y" - y')  +  y(x' - x'')  + (x''y' - x'y'') = 0

comparing with ax + by + c

a = y" - y'  

b = x' - x''

c = x''y' - x'y''

Length of perpendicular drawn from origin

=    | (0 + 0 +  x''y' - x'y'' )/ √( (y" - y') ² +  (x' - x'')² ) |

=| ( x''y' - x'y'') / √( (y" - y') ² +  (x' - x'')² ) |

The length of perpendicular drawn from origin on the line joining (x' , y') and (x" , y") is :  | ( x''y' - x'y'') / √( (y" - y') ² +  (x' - x'')² ) |

Learn More:

a straight line is parallel to the line 3x-y-3=0 and 3x-y+5=0 and lies ...

https://brainly.in/question/12891227

Find the coordinates of a point from the line x+y+3=0, whose ...

https://brainly.in/question/22471571