Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the vertices and <img alt="\mathrm{B}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmat

If the vertices \mathrm{A} and \mathrm{B} of a triangle \mathrm{ABC} are given by \mathrm{(2,5)} and \mathrm{(4,-11)} and \mathrm{C} moves along the line \mathrm{L_{1}: 9 x+7 y+4=0}, the locus of the centroid of the triangle \mathrm{ABC} is a straight line parallel to

Option: 1

\mathrm{A B}


Option: 2

\mathrm{CA}


Option: 3

\mathrm{BC}


Option: 4

\mathrm{L_{1}}


Answers (1)

best_answer

Let \mathrm{(h, k)} be the centroid of the given triangle \mathrm{A B C} with coordinates of \mathrm{ C} as (\mathrm{ \alpha, \beta} ) then

\mathrm{ h=\frac{\alpha+2+4}{3}, k=\frac{\beta+5-11}{3}}

\mathrm{ \Rightarrow \alpha = 3h-6,\beta = 3k+6 }
\mathrm{ \text { Since } C(\alpha, \beta) \text { lies on } L_{1}: 9 x+7 y+4=0}
\mathrm{ 9(3 h-6)+7(3 k+6)+4=0}
\mathrm{ \Rightarrow \quad 3(9 h+7 k)-8=0}

so that locus of \mathrm{ (h, k)} is \mathrm{ 9 x+7 y-8 / 3=0}, which is parallel to \mathrm{ L_{1}}.

Posted by

Deependra Verma

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

JEE Main 2026 application correction begins on jeemain.nta.nic.in; edit details by December 2
anam-khan

JEE Mains 2026 LIVE: NTA to conduct session 1 from January 21 to 30; exam pattern, syllabus
anam-khan

JEE Main 2026 correction window opens tomorrow; NTA allows exam city change

Latest Question