A(4,4), B(5,8), C( 8,8) ,D( 8,5)A(4,4),B(5,8),C(8,8),D(8,5)
Distance between two points:
D= sqrt((x_1-x_2)^2+(y_1-y_2)^2)D=√(x1−x2)2+(y1−y2)2
AB= sqrt ((4-5)^2+(4-8)^2)= sqrt 17AB=√(4−5)2+(4−8)2=√17
BC= sqrt ((5-8)^2+(8-8)^2)= 3BC=√(5−8)2+(8−8)2=3
CD= sqrt ((8-8)^2+(8-5)^2)= 3CD=√(8−8)2+(8−5)2=3
AD= sqrt ((4-8)^2+(4-5)^2)= sqrt 17AD=√(4−8)2+(4−5)2=√17
Adjacent sides AB and ADABandAD are of equal length.
Adjacent sides CB and CDCBandCD are of equal length
Diagonal AC= sqrt ((4-8)^2+(4-8)^2)= sqrt 32AC=√(4−8)2+(4−8)2=√32
Diagonal BD= sqrt ((5-8)^2+(8-5)^2)= sqrt 18BD=√(5−8)2+(8−5)2=√18
Slope of diagonal AC , m_1= (8-4)/(8-4)=1AC,m1=8−48−4=1
Slope of diagonal BD , m_2= (5-8)/(8-5)=-1:. m1*m2=-1
Therefore diagonal AC & BD are perpendicular to each other.
Since adjacent sides (AB , AD) and (CB,CD) are of equal
length and diagonals AC & BD are perpendicular to each
other , the vertices are of kite. [Ans]
