geometry issue

Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4). What is the shape of the quadrilateral?
a Square
b Rectangle but not a square
c Rhombus
d Parallelogram but not a rhombus
e Kite


I Guess the answer is Rhombus..

This is my approach.

Distance b/n A and B 4^2 +5^2 and B and C is (9-5)^2 +(9-4)^2 and C and D is (9-5)^2 + (9-4)^2 and D and A is 5^2 +4^2 ...So the lengths are same.



And find the slope of AB = 5/4 and BC = 4/5 and CD = 5/4 and DA= 4/5...

so AB is parallel to CD and BC is parallel to DA....but for two lines to be perpendicular the product of the slopes shld be -1..

So we don't have this condition....So rhombus...
Please share the OA....

Draw a rough sketch of the figure in the coordinate plane.

We have a "short" pair of sides that are equal to each other, and a "long" pair of sides that are equal to each other. But the sides within each pair are NOT parallel to each other. Thus, the figure cannot be a parallelogram. Eliminate A, B, C, and D! (Squares, rectangles, and rhombi are all types of parallelograms).

Choose E.

___________

A kite is a four sided figure with a short pair of equal sides and a long pair of equal sides but where they are NOT parellel. Additionally, in a kite, one diagonal bisects (cuts in half) the other whereas in any parallelogram both diagonals bisect each other.

I think the ans is c. Rhombus.

Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4).

The midpoints of diagonal AC and diagonal BD is same i.e. (9/2, 9/2).

In a kite the point of intersection of two diagonals do not bisect both the diagonals. Hence it should be a rhombus

Operation780 wrote:I think the ans is c. Rhombus.

Vertices of a quadrilateral ABCD are A(0, 0), B(4, 5), C(9, 9) and D(5, 4).

The midpoints of diagonal AC and diagonal BD is same i.e. (9/2, 9/2).

In a kite the point of intersection of two diagonals do not bisect both the diagonals. Hence it should be a rhombus

Agree with you. I also think it should be rhombus.
Definition of Rhombus is a quarilateral with all 4 sides equal. Thats it. Here all 4 sides are equal. hence it should be a rhombus.
https://en.wikipedia.org/wiki/Rhombus