Answer:
(A) Parallelogram
Step-by-step explanation:
The given coordinates of quadrilateral ABCD are A(-4,-1) B(-2,-5), C(4, -2) and D(2,2), using the distance formula, the sides are
AB=[tex]\sqrt{(-5+1)^2+(-2+4)^2}=\sqrt{16+4}=\sqrt{20}[/tex],
BC=[tex]\sqrt{(-2+5)^2+(2+4)^2}=\sqrt{9+36}=\sqrt{45}[/tex]
CD=[tex]\sqrt{(-2-2)^2+(4-2)^2}=\sqrt{16+4}=\sqrt{20}[/tex]
DA=[tex]\sqrt{(2+1)^2+(2+4)^2}=\sqrt{9+36}=\sqrt{45}[/tex] and diagonals are:
AC=[tex]\sqrt{(-2+1)^2+(4+4)^2}=\sqrt{1+64}=\sqrt{65}[/tex] and
BD=[tex]\sqrt{(-5-2)^2+(-2-2)^2}=\sqrt{49+16}=\sqrt{65}[/tex]
Since, the opposite sides of the given quadrilateral that are )AB and DC) and (BC and DA) are equal, moreover the diagonals are also congruent.
thus, by the definition of rectangle, that the opposite sides are equal and diagonals are congruent, the given quadrilateral is rectangle.
