Home
Class 12
MATHS
If in a triangle AB=a,AC=b and D,E are t...

If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC respectively, then DE is equal to

A

`(a)/(4)-(b)/(4)`

B

`(a)/(2)-(b)/(2)`

C

`(b)/(4)-(a)/(4)`

D

`(b)/(2)-(a)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
We know by fundamental theorem of proportionality that,
`DE=(1)/(2)BC`

In triangle, `BC=b-a`
Hence, `DE=(1)/(2)(b-a)`.
Promotional Banner

Topper's Solved these Questions

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise VECTOR ALGEBRA EXERCISES 1: Single Option Correct Type Questions|1 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|7 Videos

  • VECTOR ALGEBRA

    ARIHANT MATHS|Exercise Exercise For Session 3|11 Videos

  • TRIGONOMETRIC FUNCTIONS AND IDENTITIES

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

Similar Questions

Explore conceptually related problems

ABC is an isosceles triangle in which AB = AC. If D and E are the mid-points of AB and respectively, prove that B,C,D and E are concyclic.

Dand E are the mid-points of the sides AB and AC of DeltaABC and O is any point on side BC. O is joined to A. If P and Q are the mid-points of OB and OC respectively, then DEQP is

ABC is any triangle and D,E,F are the mid-points of sides vec(BC),vec(CA) and vec(AB) respectively. Express the vec (BE) and vec (CF) as linear combination of vectors vec (AB) and vec (AC) .

In DeltaABC , E and F are the mid-points of AC and AB respectively. The altitude AP to BC intersects FE at Q. Prove that AQ = QP.

D and E are the mid-points of the sides AB and AC respectively of DeltaABC . DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is

In given Fig. , DeltaABC is isosceles with AB = AC. D, E, F are the mid-points of sides BC, AC and AB respectively. Show that the line segment AD is perpendicular to the line segment EF and is bisected by it.

In given Fig. , DeltaABC is isosceles with AB = AC. D, E, F are the mid-points of sides BC, AC and AB respectively. Show that the line segment AD is perpendicular to the line segment EF and is bisected by it.

In a triangle, P, Q and R are mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

ABCD is a quadrilateral in which P,Q,R and S are the mid points of sides AB,BC,CD and DA respectively AC is a diagonal show that: SR||AC and SR=1/2AC

ARIHANT MATHS-VECTOR ALGEBRA-Exercise (Single Option Correct Type Questions)
  1. A and B are two points. The position vector of A is 6b-2a. A point P ...

    Text Solution

    |

  2. If three points A,B and C are collinear, whose position vectors are ha...

    Text Solution

    |

  3. If in a triangle AB=a,AC=b and D,E are the mid-points of AB and AC res...

    Text Solution

    |

  4. The two adjacent sides of a parallelogram are 2hati+4hatj-5hatk and ha...

    Text Solution

    |

  5. If A,B and C are the vertices of a triangle with position vectors vec(...

    Text Solution

    |

  6. If ABCDEF is a regular hexagon then vec(AD)+vec(EB)+vec(FC) equals :

    Text Solution

    |

  7. Find the discriminant of the quadratic equation x^2+3x+2

    Text Solution

    |

  8. In a regular hexagon ABCDEF, prove that AB+AC+AD+AE+AF=3AD.

    Text Solution

    |

  9. Find the dot product of the vector 2hati+3hatj+1hatk and 1hati+2hatj+3...

    Text Solution

    |

  10. If a and b are two non-zero and non-collinear vectors then a+b and a-b...

    Text Solution

    |

  11. If |veca+ vecb| lt | veca- vecb|, then the angle between veca and vecb...

    Text Solution

    |

  12. The magnitudes of mutually perpendicular forces a,b and c are 2,10 and...

    Text Solution

    |

  13. If hati-3hatj+5hatk bisects the angle between hata and -hati+2hatj+2ha...

    Text Solution

    |

  14. Find the discriminant of the quadratic equation x^2+5x+4=0 and also fi...

    Text Solution

    |

  15. Given three vectors vec a=6 hat i-3 hat j , vec b=2 hat i-6 hat ja ...

    Text Solution

    |

  16. ' I ' is the incentre of triangle A B C whose corresponding sides are ...

    Text Solution

    |

  17. If vecx and vecy are two non-collinear vectors and ABC is a triangle w...

    Text Solution

    |

  18. If vec xa n d vec y are two non-collinear vectors and a, b, and c r...

    Text Solution

    |

  19. If the resultant of two forces is equal in magnitude to one of the ...

    Text Solution

    |

  20. If vec b is a vector whose initial point divides the join of 5 hat ...

    Text Solution

    |