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)?

A(square
B(rhombus
C(kite
D(parallelogram

Answer 1

The correct answer should be Kite, I believe it is. 

Answer 2

(C) kite

Explanation:

The given coordinates of quadrilateral ABCD are A(4,4) B(5,8) C(8,8) and D(8,5). Using the distance formula,

AB=
`\sqrt{(8-4)^(2)+(5-4)^2}=√(16+1)=√(17)`,

BC=
`√((8-8)^2+(8-5)^2)=√(0+9)=3`,

CD=
`√((8-5)^2+(8-8)^2)=√(9+0)=3` and

DA=
`√((5-4)^2+(8-4)^2)=√(1+16)=√(17)`

Since, the Two disjoint pairs of consecutive sides are congruent as AB=DA and BC=CD.

Thus, by definition of kite, that Two disjoint pairs of consecutive sides are congruent, the given quadrilateral is a kite.