Home
Class 9
MATHS
The vertices of the triangle ABC are A (...

The vertices of the triangle ABC are A (3,0), B (0,6) and C (0,6). The sides `bar(AB)" and "bar(AC)" of "DeltaABC` are intersected by `bar(DE)` at D and E respectively into a ratio of `1:2.` Prove by coordinate geometry that `DeltaABC=9DeltaADE.`

Promotional Banner

Topper's Solved these Questions

  • AREA OF TRIANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-3 (Select the correct answer (MCQ) :)|4 Videos

  • AREA OF TRIANGLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-3 (Short-answer type question :)|5 Videos

  • AREA OF TRIANGLES

    CALCUTTA BOOK HOUSE|Exercise EXAMPLES ( Short-answer type question :)|4 Videos

  • AREA OF CIRCLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-3 (Long-answer type question :)|10 Videos

  • CIRCUMFERENCE OF CIRCLES

    CALCUTTA BOOK HOUSE|Exercise EXERCISE-2|18 Videos

Similar Questions

Explore conceptually related problems

If the vertices A,B,C of a triangle ABC are (1,2,3),(-1,0,0) ,(0,1,2) , respectively, then find angleABC .

D and E lie on the side AB and AC of DeltaABC such that DeltaDBC=DeltaEBC , Prove that DE || BC.

The midpoints of the sides of a triangle are (1, 5, -1), (0, 4, -2) and (2, 3, 4). The coordinates of its vertices are-

The coordinatea of A,B and C of the DeltaABC are (3,1), (9,7) and (-3,7) respectively. If D,E and F are the mid-point of the sides bar(BC),bar(CA)andbar(AB) respectively, then find the area of the DeltaDEF. Also show that DeltaABC=4DeltaDEF.

Find the slope of bar(AB) , where A(2, 1), B(2, 6)

If the coordinates of the vertices of a triangle ABC be (3,0), (0,6)and (6,9)and if D and E respectively divide overline(AB) and overline(AC) internally in the ratio 1:2 , then show that the area of DeltaABC=9 x the area of DeltaADE .

A (2,0) B(4,4) and C (6,2) are the vetices of the triangleABC . The mid - points of bar(BC) , bar(CA) and bar(AB) are D (5,3), E(4,1) and F(3,2) respectively. Then find the length of the three medians.

B is a vertex of the isosceles triangle ABC. D and E are the mid-points of AB and AC. If BE and CD intersects each other at F prove that DeltaBDE=3DeltaDEF .

The coordinates of the centroid of the triangle ABC are ( 1 , 1, 1) , if the coordinates of B and C are ( 1 , 1, 2) and ( -1 , 7 , -6) respectively , then find the coordiantes of the vertex A .

The coordinates of the points A,B,C D are respectively (6,3) , (-3,5) , (4,-2) and (x,3x), if ("area of the"DeltaDBC)/("area of the"DeltaABC)=(1)/(2) , find x.

CALCUTTA BOOK HOUSE-AREA OF TRIANGLES-Long-answer type questions :
  1. For what value of k the points (1,-1), (2,-1) and (k,-1) are collinear...

    Text Solution

    |

  2. Prove that the line segment obtained by joining the points (1,2) and (...

    Text Solution

    |

  3. Prove that the mid-point of the line segment obtained by joining the p...

    Text Solution

    |

  4. Find the area of the quadrilateral formed by the points (1,4), (-2,1),...

    Text Solution

    |

  5. The coordinates of A, B and C are (3,4), (-4,3) and (8,-6) respectivel...

    Text Solution

    |

  6. The coordinates of A of the DeltaABC are (2,5) and the coordinates of ...

    Text Solution

    |

  7. A (-1,5), B (3,1) and C (5,7) are the vertices of the DeltaABC. D,E an...

    Text Solution

    |

  8. The coordinates of the points A,B,C,D are (0,-1),(-1,2),(15,2) and (4,...

    Text Solution

    |

  9. The vertices of the triangle ABC are A (3,0), B (0,6) and C (0,6). The...

    Text Solution

    |

  10. Find the area of the triangle with vertices at (a,(1)/(a)),(b,(1)/(b))...

    Text Solution

    |

  11. Locate the number 1.4 on the number line by the method of successive ...

    Text Solution

    |

  12. The coordinates of A, B and C of the DeltaABC are (3,1), (9,7) and (-3...

    Text Solution

    |

  13. If the coordinates of A, B, C and D are (6,3), (-3,5), (4,-2) and (x,3...

    Text Solution

    |

  14. If the point (a,b), (a',b') and (a-a',b-b') are collinear, then prove ...

    Text Solution

    |

  15. Prove that (a,b + c), (b,a + c) and (c, a + b) are collinear.

    Text Solution

    |

  16. If P (-2,3), Q (4,-5) and R (-3,1) are the three consecutive vertices ...

    Text Solution

    |

  17. Four vertices of a quadrilateral are (-5,-5), (2,-4), (3,2) and (-2,3)...

    Text Solution

    |

  18. Four vertices of a quadrilateral are (1,2), (-5,6), (7,-4) and (k,-2) ...

    Text Solution

    |

  19. Four vertices of a quadrilateral are A (-1,6) B (-2.-4), C (3,-2) and ...

    Text Solution

    |