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.

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • CONSTRUCTIONS

    RD SHARMA ENGLISH|Exercise All Questions|32 Videos

  • PAIR OF LINEAR EQUATIONS IN TWO VARIABLES

    RD SHARMA ENGLISH|Exercise All Questions|391 Videos

Similar Questions

Explore conceptually related problems

ABCD is a rectangle formed by the points A(1,\ 1), B(1,\ 4), C(5,\ 4) and 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 your answer.

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.

ABCD 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.

If points A(5,\ p),\ \ B(1,\ 5),\ \ C(2,\ 1) and D(6,\ 2) form a square A B C D , then p= (a) 7 (b) 3 (c) 6 (d) 8

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 Q . Prove that A Q=Q P .

The points A(2,\ 0),\ \ B(9,\ 1),\ \ C(11 ,\ 6) and D(4,\ 4) are the vertices of a quadrilateral A B C D . Determine whether A B C D is a rhombus or not.

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

M ,\ N\ a n d\ P are the mid-points of A B ,\ A C\ a n d\ B C respectively. If M N=3c m ,\ N P=3. 5 c m\ a n d\ M P=2. 5 c m , calculate B C ,\ A B\ a n d\ A C

The figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a (a) parallelogram (b) rectangle (c)square (d) rhombus

Home
Profile