Parallelogram ABCDABCDA, B, C, D has the following vertices: A(0,8)A(0,8)A, left parenthesis, 0, comma, 8, right parenthesis B(8
,4)B(8,4)B, left parenthesis, 8, comma, 4, right parenthesis C(2,-8)C(2,−8)C, left parenthesis, 2, comma, minus, 8, right parenthesis D(-6,-4)D(−6,−4)D, left parenthesis, minus, 6, comma, minus, 4, right parenthesis Is parallelogram ABCDABCDA, B, C, D a rectangle, and why?
(Choice A)
A
Yes, because AB=ADAB=ADA, B, equals, A, D and BC=CDBC=CDB, C, equals, C, D, and ABCDABCDA, B, C, D is a parallelogram.
(Choice B)
B
Yes, because \overline{BC}
BC
start overline, B, C, end overline is perpendicular to \overline{AB}
AB
start overline, A, B, end overline, and ABCDABCDA, B, C, D is a parallelogram.
(Choice C)
C
No, because \overline{AB}
AB
start overline, A, B, end overline is shorter than \overline{AD}
AD
start overline, A, D, end overline.
(Choice D)
D
No, because \overline{BC}
BC
start overline, B, C, end overline is not perpendicular to \overline{AB}
AB
start overline, A, B, end overline.
