The points $A ( - 1,3 ) , B ( 2 , - 1 ) , C ( 3,6 ) , \text { and } D ( 6,2 )$ are vertices of a quadrilateral. Is the quadrilateral a rectangle?
A) Yes
B) No

Question

Quizplus · Accepted Answer

The diagonals of a rectangle are equal and bisect each other. Here, the diagonals are $AC$ and $BD$.$$AC = \sqrt{(-1-3)^2+(3-6)^2} = \sqrt{(-4)^2+(-3)^2} = \sqrt{16+9} = \sqrt{25} = 5$$$$BD = \sqrt{(2+1)^2+(-1-2)^2} = \sqrt{(3)^2+(-3)^2} = \sqrt{9+9} = \sqrt{18} = 3\sqrt{2}$$Since the diagonals are not equal, the quadrilateral is not a rectangle.

The Points A(−1,3),B(2,−1),C(3,6), and D(6,2)A ( - 1,3 ) , B ( 2 , - 1 ) , C ( 3,6 ) , \text { and } D ( 6,2 )A(−1,3),B(2,−1),C(3,6), and D(6,2)

The Points $A ( - 1,3 ) , B ( 2 , - 1 ) , C ( 3,6 ) , \text { and } D ( 6,2 )$