Question

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.

Answer 1

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.

Step-by-step explanation:

I did it on khan academy and I got it right

Answer 2

By calculating the slopes of the lines AB, BC, CD and DA using the points given and confirming that they are perpendicular, we can verify that parallelogram ABCD is indeed a rectangle. The correct answer is option B.

Step-by-step explanation:

The subject of the question is whether or not parallelogram ABCD is a rectangle. A rectangle is a specific type of parallelogram where all angles are 90 degrees, meaning its diagonals are perpendicular to each other. In this case, we're given the vertices A(0,8), B(8,4), C(2,-8), D(-6,-4). With this information, we calculate the slopes between AB and BC or CD and DA to verify if they're perpendicular. The slope of a line between two points (x1,y1) and (x2,y2) is given by the formula m=(y2-y1)/(x2-x1). Therefore, we find the slopes as follows: slope AB=(4-8)/(8-0)=-.5, slope BC=(-8-4)/(2-8)=-2, slope CD=(-4+8)/(-6-2)=1, slope DA=(8+4)/(0+6)=2. Since the slopes of AB and BC, as well as CD and DA, are the negatives of the reciprocals of each other, they indeed are perpendicular. Therefore, we can confirm that parallelogram ABCD is a rectangle, and the correct option is (Choice B) 'Yes, because BC is perpendicular to AB, and ABCD is a parallelogram'.

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