Home
Class 12
MATHS
If P(1,2), Q(4,6), R(5,7) and S(a, b) ar...

If `P(1,2), Q(4,6), R(5,7)` and `S(a, b)` are the vertices of a parallelogram `P Q R S`, then

A

`a=2, b=4`

B

`a=3, b=4`

C

`a=2, b=3`

D

`a=3, b=5`

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • COMPLEX NUMBERS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|306 Videos
  • Definite Integrals and its Application

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|453 Videos

Similar Questions

Explore conceptually related problems

If P(2, 4), Q(0, 3), R(3, 6), and S(5, y) are the vertices of a parallelogram PQRS, value of y is

The points P(2,3) , Q(3, 5), R(7, 7) and S(4, 5) are such that:

Let O(0,0), P(3,4), Q(6,0) be the vertices of the triangle O P Q . The point R inside the triangle O P Q is such that the triangle O P R, P Q R and O Q R are of equal area. The coordinates of R are

IF P,Q,R and S are respectively the mid-points of the sides of a parallelogram ABCD show are (PQRS) = 1/2 ar (ABCD)

If P=(1,0), Q=(-1,0) and R=(2,0) are three given points, then the locus of S satisfying the relation S Q^(2)+S R^(2)=2 S P^(2) is

Sum P + Q + R is :

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.

Given that p(1,2,-4) , Q (5,4, -6) and R (0,8,-10) are collinear find the ratio in which Q divides PR

If in an A.P. S_(n) = qn^(2) and S_(m) = qm^(2) , where S_(r ) denotes the sum of r terms of the A.P. , then S_(q) equals :

The vertices of trianglePQR are P(2,1),Q(-2,3) and R(4,5). Find the equation of the median through the vertex R.

HIMALAYA PUBLICATION-COORDINATE SYSTEMS, LOCUS AND STRAIGHT LINES-QUESTION BANK
  1. A line passes through (2,2) and is perpendicular to the line 3x+y=3 ...

    Text Solution

    |

  2. If P=(1,0), Q=(-1,0) and R=(2,0) are three given points, then the locu...

    Text Solution

    |

  3. If P(1,2), Q(4,6), R(5,7) and S(a, b) are the vertices of a parallelog...

    Text Solution

    |

  4. The diagonals of a parallelogram P Q R S are along the lines x+3 y=4 a...

    Text Solution

    |

  5. If the vertices P, Q, R are rational points which of the following poi...

    Text Solution

    |

  6. If the lines x-y-1=0,4 x+3 y=k and 2 x-3 y+1=0 are concurrent then k=

    Text Solution

    |

  7. The centroid of a triangle formed by the points (0, 0), (cos theta, si...

    Text Solution

    |

  8. The orthocentre of the triangle formed by (8,0) , (4,6) with the origi...

    Text Solution

    |

  9. The foot of the perpendicular from (-2,3) to the line 2 x-y-3=0 is

    Text Solution

    |

  10. The locus of the point of the portion of the line x cos alpha-ysin alp...

    Text Solution

    |

  11. The value of lambda for which the lines 3 x+4 y=5, 5 x+4 y=4 and lambd...

    Text Solution

    |

  12. Three vertices of a parallelogram taken in order are (-1,-6),(2,-5) an...

    Text Solution

    |

  13. The angle between the lines 2 x-y+3=0 and x+2 y+3=0 is

    Text Solution

    |

  14. The centroid of the triangle is (2,7) and two of its vertices are (4,8...

    Text Solution

    |

  15. The inclination of the line through (-3,6) and the midpoint of the lin...

    Text Solution

    |

  16. A point moves such that the area of the triangle formed by it with the...

    Text Solution

    |

  17. The area bounded by the curves x+2|y|=1 and x=0 is

    Text Solution

    |

  18. The foot of the perpendicular from the point (2,4) upon x+y=4 is

    Text Solution

    |

  19. A (1, 3) and C(7, 5) are two opposite vertices of a square. The equati...

    Text Solution

    |

  20. Distance between the parallel lines y=2 x+7 and y=2 x+5 is

    Text Solution

    |