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shubhankar sinha Grade:
        

let algebraic sum of perpendicular distances from points (2,0) (0,2) (1,1) to a variable straight line be zero then line passes through a fixed point whose coordinates are

7 years ago

Answers : (2)

Askiitians Expert Soumyajit IIT-Kharagpur
28 Points
										

Dear Shubhankar Sinha,


Ans:- Let the eq of the line be ax+by+c=0


it's distances from the three points are


D1=(2a+0b+c)/K..................(1)


D2=((0a+2b+c)/K...................(2)


D3=(a+b+c)/K.......................(3)


Where K=√(a²+b²)


Adding 1, 2, 3 we get


D1+D2+D3=(3a+3b+3c)/K


                 =3(a+b+c)/K


As the sum is 0 hence a+b+c=0


So, the line passes through theFixed point (1,1)         [ ax+by+c=0  putting (1,1) point in x,y we get a1+b1+c=a+b+c=0]


 


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All the best Shubhankar Sinha !!!


 



Regards,


Askiitians Experts
Soumyajit Das IIT Kharagpur

7 years ago
Aisha D'souza
26 Points
										
let the algebraic sum of the perpendicular distance from (3,0),(0,3) and (2,2) to a variable line is zero, then the line passes through a fixed point whose co-ordinates are?
one year ago
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