Home
Class 10
MATHS
The three vertices of a parallelogram ta...

The three vertices of a parallelogram taken in order are `-1,0),(3,1)a n d(2,2)` respectively. Find the coordinates of the fourth vertex.

Text Solution

Verified by Experts

Let A(-1, 0), B(3, 1), C(2, 2) and D(x, y) be the vertices of a parallelogram ABCD taken in order.
Since, the diagonals of a parallelogram bisect each other.
Then, Coordinates of the mid-point of AC=Coordinates of the mid-point of BD
`((-1+2)/2,(0+2)/2)=((3+x)/2, (1+y)/2)` ...
Promotional Banner

Topper's Solved these Questions

  • CONSTRUCTIONS

    RD SHARMA|Exercise All Questions|21 Videos
  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    RD SHARMA|Exercise All Questions|390 Videos

Similar Questions

Explore conceptually related problems

(iv) The three vertices of a parallelogram are taken in order (-1;0);(3;1) and (2;2) respectively.Find the coordinates of 4th vertex.

The three vertices of a parallelogram ABCD taken in order are A(3, -4), B(-1, -3) and C(-6, 2). Find the coordinates of the fourth vertex D.

Three vertices of a parallelogram,taken in order,are (-1,-6),(2,-5) and (7,2). Write the coordinates of its fourth vertex.

If A (3, 5), B (-3, - 4), C (7, 10) are the vertices of a parallelogram taken in the order, then the co-ordinates of the fourth vertex are

The coordinates of three consecutive vertices of a parallelogram are (1, 3), (-1, 2) and (2, 5). Then find the coordinates of the fourth vertex.

The co-ordinates of three consecutive vertices of a parallelogram are (-1,0), (3, 1) and (2, 2). Find the co-ordinates of fourth vertex of the parallelogram.

If three vertices of a parallelogram taken in order are (-1, 0), (3, 2) and (2, 3) then area of the parallelogram is

The three vertices of a parallelogram ABCD are A(-1,3,4), B(2,-1,3) and C(5,1,2). Find the co-ordinates of its 4th vertex D.

RD SHARMA-COORDINATE GEOMETRY-All Questions
  1. Prove that the point (-2,-1),(1,0),(4,3)a n d(1,2) are the vertices of...

    Text Solution

    |

  2. The three vertices of a parallelogram taken in order are -1,0),(3,1)a ...

    Text Solution

    |

  3. If the point C(-1,2) divides internally the line segment joining A(2,5...

    Text Solution

    |

  4. Determine the ratio in which the line 3x + y - 9 = 0 divides the se...

    Text Solution

    |

  5. The coordinates of one end point of a diameter of a circle are (4,-1) ...

    Text Solution

    |

  6. If A(5,-1),B(-3,-2)a n d(-1,8) are the vertices of triangle ABC, find ...

    Text Solution

    |

  7. Of A(-2,-1),B(a ,0),C(4, b) and D(1,2) are the vertices of a parallelo...

    Text Solution

    |

  8. if the coordinates of the mid points of the Sides of a triangle are (...

    Text Solution

    |

  9. Prove analytically that the line segment joining the middle points of ...

    Text Solution

    |

  10. Prove that the lines joining the middle points of the opposite sides o...

    Text Solution

    |

  11. The vertices of a A B C are A(5,5),B(1,5)a n dC(9,1) . A line is draw...

    Text Solution

    |

  12. If the coordinates of the mid-points of the sides of a triangle are (3...

    Text Solution

    |

  13. A(3,2)a n dB(-2,1) are two vertices of a triangle ABC whose centroid G...

    Text Solution

    |

  14. If the coordinates of the mid-points of the sides of a triangle are (1...

    Text Solution

    |

  15. Prove that the area of triangle whose vertices are (t , t-2),(t+2, t+2...

    Text Solution

    |

  16. For what value of k are the points (k ,2-2k)(-k+1,2k)a n d(-4-k ,6-2k)...

    Text Solution

    |

  17. Prove that the coordinates of the centre of the circle inscribed in th...

    Text Solution

    |

  18. If the points P ,Q(x ,7),R ,S(6, y) in this order divide the line segm...

    Text Solution

    |

  19. If A(2,2),B(-4,-4)a n dC(5,-8) are the vertices of a triangle, then th...

    Text Solution

    |

  20. The midpoint P of the line segment joining the points A(-10, 4) and B(...

    Text Solution

    |