IBV4 Quadrilateral OABC: O(0, 0), A(5, 1), B(10, 5), C(2, 7)

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In summary, the perimeter of IBV4 Quadrilateral OABC is 37.51 units. It is a parallelogram and the area is 43.33 square units. It is not a regular quadrilateral, but has some properties of one. The coordinates of the midpoints of the sides are (2.5 , 0.5), (7.5 , 3), (6 , 6), and (1 , 3.5).
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karush
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View attachment 1212

wasn't sure about $\overrightarrow{AC}$
 
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Looks good to me. :D
 
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MarkFL said:
Looks good to me. :D

thanks to MHB ...making some progress ... (Wasntme)
 

FAQ: IBV4 Quadrilateral OABC: O(0, 0), A(5, 1), B(10, 5), C(2, 7)

What is the perimeter of the IBV4 Quadrilateral OABC?

The perimeter of a quadrilateral is the total length of all its sides. To find the perimeter of IBV4 Quadrilateral OABC, we need to add the lengths of all four sides together. Using the distance formula, we can calculate the length of each side: OA = √(5^2 + 1^2) = √26, AB = √(10^2 + 5^2) = √125, BC = √(2^2 + 7^2) = √53, and CO = √(2^2 + 7^2) = √53. Therefore, the perimeter of IBV4 Quadrilateral OABC is √26 + √125 + √53 + √53 = 11.77 + 11.18 + 7.28 + 7.28 = 37.51 units.

What type of quadrilateral is IBV4 Quadrilateral OABC?

Based on its coordinates, we can determine that IBV4 Quadrilateral OABC is a parallelogram. This is because opposite sides of a parallelogram are equal in length and parallel to each other. In this case, we can see that OA is equal in length to BC and AB is equal in length to CO. Additionally, we can draw a line connecting points OB and AC, and see that it is parallel to both OA and BC.

What is the area of IBV4 Quadrilateral OABC?

The area of a quadrilateral can be calculated using the formula A = ½ * (d₁ * d₂), where d₁ and d₂ are the lengths of the diagonals. In this case, we can find the length of the diagonals using the distance formula: d₁ = √(5^2 + 7^2) = √74 and d₂ = √(10^2 + 1^2) = √101. Therefore, the area of IBV4 Quadrilateral OABC is ½ * (√74 * √101) = ½ * 8.60 * 10.05 = 43.33 square units.

Is IBV4 Quadrilateral OABC a regular quadrilateral?

A regular quadrilateral, also known as a square, has all four sides equal in length and all four angles equal in measure. In this case, we can see that IBV4 Quadrilateral OABC is not a regular quadrilateral, as its sides and angles are not all equal. However, it is still a parallelogram and has some properties of a regular quadrilateral, such as having opposite sides equal in length and parallel to each other.

How do you find the coordinates of the midpoints of the sides of IBV4 Quadrilateral OABC?

To find the coordinates of the midpoints of the sides of a quadrilateral, we can use the midpoint formula: (x₁+x₂)/2 , (y₁+y₂)/2. In this case, the coordinates of the midpoint of OA would be ((0+5)/2 , (0+1)/2) = (2.5 , 0.5). Similarly, the coordinates of the midpoints of AB, BC, and CO would be (7.5 , 3), (6 , 6), and (1 , 3.5), respectively.

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