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?  Choose one:
A) Square
B) Rectangle but not a square
C) Rhombus
D) Parallelogram but not a rhombus
E) Kite
Explanatory Answer   The lengths of the four sides, AB, BC, CD and DA are all equal to 41−−√41. (Computation given in the last paragraph)   Hence, the given quadrilateral is either a Rhombus or a Square.   How to determine whether the quadrilateral is a square or a rhombus?   The diagonals of a square are equal. The diagonals of a rhombus are unequal.   Compute the lengths of the two diagonals AC and BD.   The length of AC is √162 and the length of BD is 2–√2.   As the diagonals are not equal and the sides are equal, the given quadrilateral is a Rhombus.   Rhombushoice Rhombus
<result>C</result>
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?