Home
Class 12
MATHS
P and Q are points on the line joining A...

`P` and `Q` are points on the line joining `A(-2,5)` and `B(3,1)` such that `A P=P Q=Q B` . Then, the distance of the midpoint of `P Q` from the origin is 3 (b) `(sqrt(37))/2` (b) 4 (d) 3.5

A

3

B

`sqrt(37//2)`

C

4

D

`3.5`

Text Solution

Verified by Experts

The correct Answer is:
B
The midpoint of PQ is the midpoint of AB which is `R(1//2,3)`. Therefore,
`OR=sqrt((1)/(4)+9)=sqrt(37)/(2)` .
Promotional Banner

Topper's Solved these Questions

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Multiple)|13 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise (Comprehension)|10 Videos

  • COORDINATE SYSYEM

    CENGAGE|Exercise Exercise 1.6|9 Videos

  • COORDINATE SYSTEM

    CENGAGE|Exercise Multiple Correct Answers Type|2 Videos

  • CROSS PRODUCTS

    CENGAGE|Exercise DPP 2.2|13 Videos

Similar Questions

Explore conceptually related problems

P and Q are points on the line joining A(-2,5) and B(3,1) such that A P=P Q=Q B . Then, the distance of the midpoint of P Q from the origin is (a) 3 (b) (sqrt(37))/2 (c) 4 (d) 3.5

Let P and Q be point on the line joining A(5,6) and B (3, -4) such that AP=PQ=QB. Then the midpoint of PQ is

Find the position vector of the midpoint of the vector joining the points P(2, 3, 4) and Q(4, 1 -2)

P is a point on the line y+2x=1, and Q and R 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 ((a)/(3),(b)/(2)) is the mid - point of the line segment joining A(-4,3) and B(-2,4) then (a,b) is

If P(x ,y ,z) is a point on the line segment joining Q(2,2,4)a n d R(3,5,6) such that the projections of vec O P on the axes are 13/5, 19/5 and 26/5, respectively, then find the ratio in which P divides Q Rdot

The image of P(a ,b) on the line y=-x is Q and the image of Q on the line y=x is R . Then the midpoint of P R is (a) (a+b ,b+a) (b) ((a+b)/2,(b+2)/2) (c) (a-b ,b-a) (d) (0,0)

Let O(0,0),P(3,4), and Q(6,0) be the vertices of triangle O P Q . The point R inside the triangle O P Q is such that the triangles O P R ,P Q R ,O Q R are of equal area. The coordinates of R are (a) (4/3,3) (b) (3,2/3) (c) (3,4/3) (d) (4/3,2/3)

At what angle do the two forces (P+Q) and (P-Q) act so that the resultant is sqrt(3P^(2)+Q^(2)) ?

CENGAGE-COORDINATE SYSYEM -Exercise (Single)
  1. The polar coordinates equivalent to (-3,sqrt3) are

    Text Solution

    |

  2. If the point (x1+t(x2-x1),y1+t(y2-y1)) divides the join of (x1,y1) and...

    Text Solution

    |

  3. P and Q are points on the line joining A(-2,5) and B(3,1) such that A ...

    Text Solution

    |

  4. In triangle ABC, angle B is right angled, AC=2 and A(2,2), B(1,3) then...

    Text Solution

    |

  5. One vertex of an equilateral triangle is (2,2) and its centroid is (-2...

    Text Solution

    |

  6. ABCD is a rectangle with A(-1,2),B(3,7) and AB:BC=4:3. If P is the cen...

    Text Solution

    |

  7. If (2,-3), (6,-5) and (-2,1) are three consecutive vetcies of a rohomb...

    Text Solution

    |

  8. If A and B are square matrix of same order then (A-B)^(T) is:

    Text Solution

    |

  9. Le n be the number of points having rational coordinates equidistant ...

    Text Solution

    |

  10. Draw a triangle ABC of base BC = 5.6 cm, angle A = 40^(@) and the bise...

    Text Solution

    |

  11. If A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2) then the centre of the circle...

    Text Solution

    |

  12. Statement 1: If in a triangle, orthocentre, circumcentre and centroid ...

    Text Solution

    |

  13. about to only mathematics

    Text Solution

    |

  14. If two vertices of a triangle are (-2,3) and (5,-1) the orthocentre li...

    Text Solution

    |

  15. The vertices of a triangle are (p q ,1/(p q)),(p q)),(q r ,1/(q r)), a...

    Text Solution

    |

  16. If the vertices of a triangle are (sqrt(5,)0) , (sqrt(3),sqrt(2)) , an...

    Text Solution

    |

  17. Two vertices of a triangle are (4,-3) & (-2, 5). If the orthocentre o...

    Text Solution

    |

  18. In A B C , if the orthocentre is (1,2) and the circumcenter is (0, 0)...

    Text Solution

    |

  19. A triangle A B C with vertices A(-1,0),B(-2,3/4), and C(-3,-7/6) has i...

    Text Solution

    |

  20. If a triangle A B C ,A-=(1,10), circumcenter -=(-1/3,2/3), and orthoce...

    Text Solution

    |