Home
Class 12
MATHS
The medians AD and BE of the triangle wi...

The medians AD and BE of the triangle with vertices A(0,b),B(0,0) and C(a,0) are mutually perpendicular if

A

`b=sqrt(2)a`

B

`a=sqrt(2)b`

C

`b=-sqrt(2)a`

D

`a=-sqrt(2)b`

Text Solution

Verified by Experts

The correct Answer is:
B, D
Promotional Banner

Topper's Solved these Questions

  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise PROBLEM SET(2)(TRUE AND FALSE)|7 Videos

  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise PROBLEM SET(2)(fill in the blanks)|2 Videos

  • RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE

    ML KHANNA|Exercise PROBLEM SET(1)(FILL IN THE BLANK)|3 Videos

  • PROPERTIES OF TRIANGLES

    ML KHANNA|Exercise Self Assessment Test (Multiple Choise Questions)|34 Videos

  • SELF ASSESSMENT TEST

    ML KHANNA|Exercise OBJECTIVE MATHEMATICS |16 Videos

Similar Questions

Explore conceptually related problems

The medians AD and BE of the triangle with vertices A(0,b),B(0,0) and C(a,0) are mutually perpendicular. Prove that a^2=2b^2 .

The medians A D\ a n d\ B E of a triangle with vertices A(0, b),\ B(0,0)\ a n d\ C(a ,0) are perpendicular to each other, if a=b/2 b. b=a/2 c. a b=1 d. a=+-sqrt(2)b

The medians BE and AD of a triangle with vertices A(0,b),B(0,0) and C(a,0) are perpendicular to each other,if.

If the medians PT and RS of a triangle with vertices P (0, b), Q (0, 0) and R (a, 0) are perpendicular to each other, which of the following satisfies the relationship between a and b?

The area of a triangle with vertices A(3,0),B(7,0) and C(8,4) is

The area of a triangle with vertices A(5, 0), B(8, 0) and C(8, 4) in square units is

Find the lengths of the medians of the triangle with vertices A(0,0,6),B(0,4,0)and C(6,0,0)

Circumradius of the triangle with vertices (2a,0),(2a,2b),(0,2b) is

ML KHANNA-RECTANGULAR CARTESIAN CO-ORDINATE SYSTEM AND THE STRAIGHT LINE-PROBLEM SET(2)(MULTIPLE CHOICE QUESTIONS)
  1. If A(9,-9),B(1,3) are the ends of a right angled isosceles triangle t...

    Text Solution

    |

  2. A triangle ABC right angled at A has points A and B as (2, 3) and (0, ...

    Text Solution

    |

  3. The medians AD and BE of the triangle with vertices A(0,b),B(0,0) and ...

    Text Solution

    |

  4. The line 4x+y=lamda cuts the axes of co ordinates at A and B. If C is ...

    Text Solution

    |

  5. The equations of perpendicular bisectors of the sides AB and AC of a ...

    Text Solution

    |

  6. The side AB of an isosceles triangle is along the axis of x with verti...

    Text Solution

    |

  7. A straight line through the point (2,2) intersects the line sqrt(3)x+y...

    Text Solution

    |

  8. The line ax+by+c=0 intersects the line x cos alpha+y sinalpha=c at the...

    Text Solution

    |

  9. A line passes through (2,2) and is perpendicular to the line 3x+y=3 .I...

    Text Solution

    |

  10. If the lines x(sinalpha+sinbeta)-ysin(alpha-beta)=3 and x(cosalpha+c...

    Text Solution

    |

  11. The lines p(p^2+1)x-y+q=0 and (p^2+1)^2x+(p^2+1)y+2q=0 are perpendicul...

    Text Solution

    |

  12. The points A(x,y), B(y, z) and C(z,x) represents the vertices of a rig...

    Text Solution

    |

  13. If A(1,1),B(sqrt(3)+1,2) and C(sqrt(3),sqrt(3)+2) be three vertices of...

    Text Solution

    |

  14. A(-2,4),B(-1,2),C(1,2) and D(2,4) are the vertices of a quadrilateral....

    Text Solution

    |

  15. The four sides of a quadrilateal are given by xy(x-2)(y-3)=0. A line i...

    Text Solution

    |

  16. The vertex C of a triangle ABC moves on the line L-=3x+4y+5=0. The c...

    Text Solution

    |

  17. The three lines 4x - 7y + 10 , x + y = 5 and 7x+ 4y = 15 form the sid...

    Text Solution

    |

  18. The equation of the base of an equilateral triangle is x+y=2 and the v...

    Text Solution

    |

  19. The distance between the lines 4x+3y=11 and 8x+6y=15 is

    Text Solution

    |

  20. The distance between the lines 3x+4y=9 and 6x+8y=15 is

    Text Solution

    |