Home
Class 10
MATHS
A B C D is a rectangle formed by join...

`A B C D` is a rectangle formed by joining the points `A(-1,\ -1),\ \ B(-1,\ 4),\ \ C(5,\ 4)` and `D(5,\ -1)dot` `P ,\ Q ,\ R` and `S` are the mid-points of sides `A B ,\ B C ,\ C D` and `D A` respectively. Is the quadrilateral `P Q R S` a square? a rectangle? or a rhombus? Justify your answer.

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

ABCD is a rectangle formed by the points A(1," "1)," "B(1," "4)," "C(5," "4)" "a n d" "D(5," "1) . P, Q, R and S are the midpoints of AB, BC, CD and DA respectively. Is the quadrilateral PQRS a square? A rectangle? or a rhombus? Justify yo

ABCD is a rhombus and P, Q, R and S are ©wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.

ABCD is rectangle formed by the points A(-1, -1), B(-1, 4), C(5, 4) and D(5, -1). If P, Q, R and S be the midpoint of AB, BC, CD and DA respectively, show that PQRS is a rhombus.

ABCD is a rectangle and P,Q,R and S are mid- points of the sides AB,BC,CD and DA respectively.Show that the quadrilateral PQRS is a rhombus.

A B C D is a rhombus and P ,\ Q ,\ R ,\ S are the mid-points of A B ,\ B C ,\ C D ,\ D A respectively. Prove that P Q R S is a rectangle.

In Fig. 32, A B C D is a rectangle of length A B=40\ c m and breadth B C=25\ c mdot If P , Q , R , S be the mid-points of the sides A B ,\ B C ,\ C D\ and \ D A respectively, find the area of the shaded region.

Show that the points A(2,-2), B(8, 4), C(5,7) and D(-1, 1) are the angular points of a rectangle.

In a A B C ,\ E\ a n d\ F are the mid-points of A C\ a n d\ A B respectively. The altitude A P\ to\ B C intersects F E\ at Qdot Prove that A Q=Q P

If D ,E ,F are the mid-points of the sides B C ,C Aa n dA B respectively of a triangle A B C , prove by vector method that A r e aof D E F=1/4(a r e aof A B C)dot

In a triangle, P ,\ Q\ a n d\ R are the mid-points of sides B C ,\ C A\ a n d\ A B respectively. If A C=21\ c m ,\ B C=29 c m\ a n d\ A B=30 c m , find the perimeter of the quadrilateral A R P Q

RD SHARMA-COORDINATE GEOMETRY-All Questions
  1. A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of A B C . Find th...

    Text Solution

    |

  2. A(4,\ 2),\ B(6,5) and C(1,\ 4) are the vertices of A B C . Find the...

    Text Solution

    |

  3. A B C D is a rectangle formed by joining the points A(-1,\ -1),\ \ ...

    Text Solution

    |

  4. Show that A(-3,\ 2),\ \ B(-5,\ -5),\ \ C(2,\ -3) and D(4,\ 4) are the ...

    Text Solution

    |

  5. Find the ratio in which the y-axis divides the line segment joining...

    Text Solution

    |

  6. If the points A(6,\ 1),\ \ B(8,\ 2),\ \ C(9,\ 4) and D(k ,\ p) are ...

    Text Solution

    |

  7. In what ratio does the point (-4,\ 6) divide the line segment jo...

    Text Solution

    |

  8. Find the coordinates of a point A , here A B is a diameter of th...

    Text Solution

    |

  9. Find the ratio in which the point P(-1,\ y) lying on the line se...

    Text Solution

    |

  10. Points P ,\ Q ,\ R and S divide the line segment joining the points...

    Text Solution

    |

  11. Find the ratio in which the point P(x ,\ 2) divides the line seg...

    Text Solution

    |

  12. Find the ratio in which the line segment joining the points A(3,\ -...

    Text Solution

    |

  13. Find the ratio in which the point P((3)/(4), (5)/(12)) divides the lin...

    Text Solution

    |

  14. Find the coordinates of the centroid of a triangle whose vertices a...

    Text Solution

    |

  15. Find the centroid of the triangle whose vertices are: (1,\ 4),\ (-1...

    Text Solution

    |

  16. Two vertices of a triangle are (1,\ 2),\ (3,\ 5) and its centroi...

    Text Solution

    |

  17. If (-2,\ 3),\ (4,\ -3) and (4,\ 5) are the mid-points of the sides ...

    Text Solution

    |

  18. In Fig. 14.40, a right triangle B O A is given. C is the mid-poi...

    Text Solution

    |

  19. Find the third vertex of a triangle, if two of its vertices are at ...

    Text Solution

    |

  20. Find the area of a triangle whose vertices are A(3,2),\ \ B(11 ,\ 8...

    Text Solution

    |