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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 : (4)

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




Where K=√(a²+b²)

Adding 1, 2, 3 we get



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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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?
2 years ago
13 Points
										Let the variable line be px+qy+1=0 then given condition P1+P2+P3=3p+3q+3=0Or p+q+1=0Condition of upper eq show that the variable line passes through the point (1,1)
6 months ago
ambuj tiwari
18 Points
										let eq.will be ax+by+c=0      now alzebric  sum of perpendicular distance will 0   so  the.  Distance is 3a+c/k+3b+c/k+2a+2b+c/k=0. And k=root of a^+b^.      Now. Take lcm and after solve we get. 5a+5b+3c=0.   Now divided by 3 to make 3is1.   5a/3+5b/3+c=0.     So.            Comparing on       The point.  Is x=5/3.  And.  y=5/3 so. (x,y)=(5/3,5/3)
2 months ago
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