Prove that the points (3, 0), (4, 5), (-1, 4) and (-2, -1), taken in order, form a rhombus. Also, find its area.
Let the Vertices of a quadrilateral are: A(3, 0), B(4, 5), C(-1, 4) and D(-2, -1),
Length of side AB =
Length of side AB =
= 
= 
units
Length of side BC =
= 
= 
units
Length of side CD =
= 
= 
units
Length of side DA =
= 
= 
units
Length of diagonal AC =
= 
= 
units
Length of side BD =
= 
= 
units
Since all sides are of equal length, therefore it is a rhombus.
Area of Rhombus = 
= 
= 
= 24 sq. units
40