Answered

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

Verified Answer :

NaLuShipper4Life

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

boffeemadrid

Answer:

(C) kite

Step-by-step 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=\(\sqrt{(8-4)^{2}+(5-4)^2}=\sqrt{16+1}=\sqrt{17}\),

BC=\(\sqrt{(8-8)^2+(8-5)^2}=\sqrt{0+9}=3\),

CD=\(\sqrt{(8-5)^2+(8-8)^2}=\sqrt{9+0}=3\) and

DA=\(\sqrt{(5-4)^2+(8-4)^2}=\sqrt{1+16}=\sqrt{17}\)

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.

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