Question 1179995: The four vertices of a quadrilateral are A (-4,5), B(1,9), C(6,5) and D(1,1). Can you help me prove the quadrilateral is a rhombus ? Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Need to show sides are equal and parallel.
Distance AB is sqrt ((diff x)^2+ (diff y)^2)=sqrt (41)
BC is also sqrt (41)
so are the other two sides. So sides have equal length.
Now show that AB and CD are parallel, by showing slopes are equal and BC and DA have equal slopes.
slope is (diff y)/(diff x) or (4/5) for AB; (-4/5) for BC; (4/5) for CD; and (-4/5) for BA.
They are parallel.
