Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Please,please help me - A point P moves on the line 2x-3y+4=0. If Q(1,4) and R(3,-2) are fixed points, then the locus of the - Co-ordinate geometry - JEE Main

A point P moves on the line 2x-3y+4=0. If Q(1,4) and R(3,-2) are fixed points, then the locus of the centroid of \Delta PQR is a line:

  • Option 1)

    with slope 3/2

  • Option 2)

    parallel to x-axis

  • Option 3)

    with slope 2/3

  • Option 4)

    parallel to y-axis

Answers (1)

best_answer

 

Centroid formula -

\left ( \frac{x_{1}+x_{2}+x_{3}}{3}, \frac{y_{1}+y_{2}+y_{3}}{3}\right )

- wherein

A(x1,y1) ; B(x2,y2) and C(x3,y3) are the vertices of  ? ABC.

 

 

Slope – point from of a straight line -

y-y_{1}=m(x-x_{1})

- wherein

m\rightarrow slope

\left ( x_{1},y_{1} \right )\rightarrow point through which line passes

 

Let the point P is (a,b)

from the concept of centroid of triangle

h = \frac{a+1+3}{3} \ and \ K = \frac{b+4-2}{3}

where (h,k) is centroid of triangle .

a= (3h-4) , b = (3k-2)

point (a,b) lies on 2x-3y+4 = 0

\therefore 2(3h-4) -3(3K-2) + 4 = 0

\Rightarrow 6h - 8 - 9K + 6 + 4 = 0

=6x -9y + 2 = 0

slope = \frac{2}{3}


Option 1)

with slope 3/2

Option 2)

parallel to x-axis

Option 3)

with slope 2/3

Option 4)

parallel to y-axis

Posted by

admin

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 2025 response sheet errors: Delhi HC allows student to apply for JEE Adv, seeks NTA explanation
anam-khan

Four Kashmiri girls defy the odds, score 99+ percentile in JEE Main 2025
anam-khan

JEE, NEET, CUET coaching centres: Assam, Rajasthan have framed laws, but will they work?

Latest Question