Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let the algebraic sum of the perpendicular distances from the points <img alt="\mathrm{A(2,0), B(0,2), C(1,1)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7BA%282%2C0%29%2C%20B%

Let the algebraic sum of the perpendicular distances from the points \mathrm{A(2,0), B(0,2), C(1,1)} to a variable straight line be zero. Then, the line passes through a fixed point
 

Option: 1

(1,0)

 


Option: 2

(1,1)
 


Option: 3

(1,2)
 


Option: 4

(2,2)


Answers (1)

best_answer

Let the line be \mathrm{l x+m y+n=0} and perpendicular distances be \mathrm{p_1, p_2, p_3} from \mathrm{A, B, C} respectively.

\mathrm{ \therefore p_1+p_2+p_3=\frac{2 l+n}{\sqrt{l^2+m^2}}+\frac{2 m+n}{\sqrt{l^2+m^2}}+\frac{l+m+n}{\sqrt{l^2+m^2}}=0 }

\mathrm{ \Rightarrow 3 l+3 m+3 n=0 }

\mathrm{ \Rightarrow l+m+n=0}

Or (1,1) lies on the line, \mathrm{l x+m y+n=0}.

Hence option 2 is correct

Posted by

manish

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

CSAB 2025 counselling dates out for special, supernumerary rounds through JEE Mains
anam-khan

'Why are they dying only in Kota': SC grills Rajasthan over surge in student suicides
anam-khan

JEE Main 2025 paper 2 final answer key out; NTA drops 4 questions, 2 from BPlanning

Latest Question