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=[tex]\sqrt{(8-4)^{2}+(5-4)^2}=\sqrt{16+1}=\sqrt{17}[/tex],
BC=[tex]\sqrt{(8-8)^2+(8-5)^2}=\sqrt{0+9}=3[/tex],
CD=[tex]\sqrt{(8-5)^2+(8-8)^2}=\sqrt{9+0}=3[/tex] and
DA=[tex]\sqrt{(5-4)^2+(8-4)^2}=\sqrt{1+16}=\sqrt{17}[/tex]
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.
