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

Question

asked Mar 26, 2017 149k views

2 Answers

PLB · Answer 1 · 2017-04-01T02:14:32+0000

Answer:

(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.