Question 864720
From the definition of a Rhombus, we know that all four sides are of equal length ,the opposite sides are parallel and the diagonals are of equal length.
we will use the following math concepts
distance (d) between two points = square root ( (x2-x1)^2 + (y2-y1)^2 )
two lines are parallel if they have the same slope (m)
m is defined as (y2 - y1) / (x2 - x1)
we are given the vertices (0,-5) (3,-4) (8,0) and (5,-1) and label them A,B,C,D
d(AB) = square root ( 3^2 + 1^2 )  = square root (10)
d(CD) = square root ( -3^2 + -1^2) = square root (10)
d(BC) = square root ( 5^2 + 4^2)   = square root (41)
d(AD) = square root ( 5^2 + 4^2)   = square root (41)
d(AC) = square root ( 8^2 + 5^2)   = square root (89)
d(BD) = square root ( 2^2 + 3^2)   = square root (13)
m(AB) = 1/3
m(CD) = -1/-3 = 1/3
m(BC) = 4/5
m(AD) = 4/5
m(AC) = 5/8
m(BD) = 3/2
AB and CD are parallel and equal length
BC and AD are parallel and equal length
AC and BD are not parallel or perpendicular and are of unequal length
this is NOT a rhombus