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 mid-points of AB, BC, CD and DA respectively. Is the quadrilateralPQRS a square? a rectangle? or a rhombus? Justify your answer
P is the mid-point of AB
Coordinates of P = (-1, 
)
Similarly coordinates of Q, R and S are (2, 4), (5, 
) and (2, -1) respectively
Length of PQ = [(-1 – 2)2 + (
)2]1/2
= 
Length of QR = [(2 – 5)2 + (
)2]1/2
= 
Length of RS = [(5 – 2)2 + (
+ 1)2]1/2
= 
Length of SP = [(2+ 1)2 + (-1 – 
)2]1/2
= 
Length of PR = [(-1- 5)2 + (
– 
)2]1/2
= 6
Length of QS = [(2 – 2)2 + (4 + 1)2]1/2
= 5
It can be observed that all sides of the given quadrilateral are of the same measure. However, the diagonals are ofdifferent lengths. Therefore, PQRS is a rhombus