Home
Class 12
MATHS
A point P moves on the line 2x-3y+4=0. I...

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

A

parallel to x-axis

B

with slope `3/2`

C

parallel to y-axis

D

with slope `2/3`

Text Solution

Verified by Experts

The correct Answer is:
D

`4x - 6y + 5 = 0`
` Q(1,3) , P (3, - 1)`
Let (h,k) be centroid
`h = (t + 1 + 3)/( 3) = ( t+ 4)/(3)`
`k = ((4t + 5)/(6) + 3 - 1)/(3) = ((4t + 5 + 12)/(6) )/(3) = (4t + 17)/(18)`
`t = 3h - 4`
` 18k - 17 = 4t`
` 18 k = 17 = 4 (3h - 4)`
` 18k - 17 = 12h - 16`
` 12h - 18k + 1 = 0`
` 12 x - 18 y + 1 = 0`
Slope ` = (12/18) = 2/3`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISION TEST - 18

    VMC MODULES ENGLISH|Exercise MATHEMATICS - SECTION 2|5 Videos

  • JEE MAIN REVISION TEST - 22 JEE - 2020

    VMC MODULES ENGLISH|Exercise MATHEMATICS|25 Videos

Similar Questions

Explore conceptually related problems

A point P moves on line 2x-3y+4=0 If Q(1,4) and R(3,-2) are fixed points, then the locus of the centroid of triangle PQR is a line: (a) with slope 3/2 (b) parallel to y-axis (c) with slope 2/3 (d) parallel to x-axis

If the vertices Pa n dQ of a triangle P Q R are given by (2, 5) and (4,-11) , respectively, and the point R moves along the line N given by 9x+7y+4=0 , then the locus of the centroid of triangle P Q R is a straight line parallel to PQ (b) QR (c) RP (d) N

The vertex C of a triangle ABC moves on the line L-=3x+4y+5=0 . The co-ordinates of the points A and B are (2,7) and (5,8) The locus of centroid of DeltaABC is a line parallel to:

Let P is a point on the line y+2x=2 and Q and R are two points on the line 3y+6x=3 . If the triangle PQR is an equilateral triangle, then its area (in sq. units) is equal to

Given three points P, Q, R with P (5, 3) and R lies on the x-axis. If equation of RQ is x-2y=2 and PQ is parallel to the x-axis, then the centroid of "Delta" PQR lies on the line (1) x-2y+1=0 (2) 2x+y-9=0 (3)2x-5y=0 (4) 5x-2y=0

A circle with centre (3alpha, 3beta) and of variable radius cuts the rectangular hyperbola x^(2)-y^(2)=9a^(2) at the points P, Q, S, R . Prove that the locus of the centroid of triangle PQR is (x-2alpha)^(2)-(y-2beta)^(2)=a^(2) .

A (-4, 2), B(0, 2) and C(-2,-4) are vertices of a triangle ABC. P, Q and R are mid-points of sides BC, CA and AB respectively. Show that the centroid of Delta PQR is the same as the centroid of Delta ABC.

Let AB be a chord of the circle x^2+y^2=r^2 subtending a right angle at the center. Then the locus of the centroid of the Delta PAB as P moves on the circle is (1) A parabola (2) A circle (3) An ellipse (4) A pair of straight lines

P is a point on the line y+2x=1, and Q and R are two points on the line 3y+6x=6 such that triangle P Q R is an equilateral triangle. The length of the side of the triangle is (a) 2/(sqrt(5)) (b) 3/(sqrt(5)) (c) 4/(sqrt(5)) (d) none of these

If P is a point on the parabola y^(2)=8x and A is the point (1,0) then the locus of the mid point of the line segment AP is

VMC MODULES ENGLISH-JEE MAIN REVISION TEST - 19-MATHEMATICS
  1. If dy/dx+3/cos^2xy=1/cos^2x,x in((-pi)/3,pi/3)and y(pi/4)=4/3," then "...

    Text Solution

    |

  2. Let d in R, and A[{:(,-2,4+d,(sin theta-2)),(,1,(sin theta)+2,d),(,5,(...

    Text Solution

    |

  3. A point P moves on the line 2x-3y+4=0. If Q(1,4) and R (3,-2) are fixe...

    Text Solution

    |

  4. The shortest distance between the point (0, 1/2) and the curve x ...

    Text Solution

    |

  5. If 5, 5r and 5r^(2) are the lengths of the sides of a triangle, then r...

    Text Solution

    |

  6. Let I=undersetaoversetbint(x^4-2x^2)dx. If is minimum, then the ordere...

    Text Solution

    |

  7. If a circle C passing through the point (4, 0) touches the circle x^(2...

    Text Solution

    |

  8. Let veca = 2hati+lambda1 hatj+3hatk, vec(b)=4hati+(3-lambda2) hatj+6ha...

    Text Solution

    |

  9. If the area enclosed between the curves y=kx^2 and x=ky^2, where kgt0,...

    Text Solution

    |

  10. An unbiased coin is tossed. If the outcome is a head then a pair of un...

    Text Solution

    |

  11. Consider a triangular plot ABC with sides AB = 7 m, BC = 5m and CA = 6...

    Text Solution

    |

  12. The mean of five observations is 5 and their variance is 9.20. If thre...

    Text Solution

    |

  13. Let f : RtoR be a function such that f(x)=x^3+x^2f'(1)+xf''(2)+f'''(3)...

    Text Solution

    |

  14. If the line 5x + 12y - 60 = 0 intersects the x-axis at the point A an...

    Text Solution

    |

  15. Let A be a point on the line vecr = (1- 5 mu) hati + (3mu - 1) hatj + ...

    Text Solution

    |

  16. The equation of a tangent to the hyperbola 9x^2 - 12y^2 = 144 paralle...

    Text Solution

    |

  17. Consider the statement: "P(n): n^(2)-n+41 is prime". Then which one of...

    Text Solution

    |

  18. The sum of all values of theta in (0,(pi)/(2)) satisfying sin^(2)2thet...

    Text Solution

    |

  19. Let nge2 be a natural number and 0ltthetaltpi//2. Then int((sin^ntheta...

    Text Solution

    |

  20. The condition that the parabolas y^2=4c(x-d) and y^2=4ax have a common...

    Text Solution

    |