What is the most precise term for quadrilateral ABCD with vertices A(4,4), B(5,8), C(8,8), and D(8,5)? square rhombus kite parallelogram

1 Answer
Binayaka C.
Jul 23, 2018

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.

Explanation:

#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)#

#AB= sqrt ((4-5)^2+(4-8)^2)= sqrt 17#

#BC= sqrt ((5-8)^2+(8-8)^2)= 3#

#CD= sqrt ((8-8)^2+(8-5)^2)= 3#

#AD= sqrt ((4-8)^2+(4-5)^2)= sqrt 17#

Adjacent sides #AB and AD# are of equal length.

Adjacent sides #CB and CD# are of equal length

Diagonal #AC= sqrt ((4-8)^2+(4-8)^2)= sqrt 32#

Diagonal #BD= sqrt ((5-8)^2+(8-5)^2)= sqrt 18#

Slope of diagonal #AC , m_1= (8-4)/(8-4)=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]

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