Question

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

Answer 1

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]