Question
The vertices of a quadrilateral ABCD are A(0, 0), B(4, 4), C(4, 8) and D(0, 4). Then, ABCD is a
Answer: Option D
A parallelogram is a quadrilateral which has two pairs of parallel sides. It can be defined as a four sided shape which has opposite sides that are both equal in length and parallel to each other.
We will now check if the given quadrilateral ABCD is a parallelogram.
• The coordinates of the vertices of the quadrilateral ABCD are A(0, 0), B(4, 4), C(4, 8) and D(0, 4).
• The length of the sides can be calculated using the distance formula.
• The distance between A and B is √((4-0)2 + (4-0)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between B and C is √((4-4)2 + (8-4)2) = √(02+42) = √(0+16) = 4
• The distance between C and D is √((4-0)2 + (8-4)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between D and A is √((0-0)2 + (4-0)2) = √(02+42) = √(0+16) = 4
From the above calculations, we can see that the lengths of the opposite sides of the quadrilateral ABCD are same, i.e. AB = CD and AD = BC. Therefore, the quadrilateral ABCD is a parallelogram.
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A parallelogram is a quadrilateral which has two pairs of parallel sides. It can be defined as a four sided shape which has opposite sides that are both equal in length and parallel to each other.
We will now check if the given quadrilateral ABCD is a parallelogram.
• The coordinates of the vertices of the quadrilateral ABCD are A(0, 0), B(4, 4), C(4, 8) and D(0, 4).
• The length of the sides can be calculated using the distance formula.
• The distance between A and B is √((4-0)2 + (4-0)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between B and C is √((4-4)2 + (8-4)2) = √(02+42) = √(0+16) = 4
• The distance between C and D is √((4-0)2 + (8-4)2) = √(42+42) = √(16+16) = √32 = 5.66
• The distance between D and A is √((0-0)2 + (4-0)2) = √(02+42) = √(0+16) = 4
From the above calculations, we can see that the lengths of the opposite sides of the quadrilateral ABCD are same, i.e. AB = CD and AD = BC. Therefore, the quadrilateral ABCD is a parallelogram.
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