To find the length of the side between point A and point B, we can use the given coordinates of points A and B on the rectangle.
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Identify the coordinates of Point A and Point B:
- The rectangle has length 80 feet and width 70 feet.
- The top left vertex of the rectangle can be labeled as (0, 70), the top right vertex (80, 70), etc.
- Point A is located 40 feet from the top left vertex along the top edge. This means point A's coordinates are (40, 70).
- Point B is located 40 feet from the bottom right vertex along the right edge. This means point B's coordinates are (80, 30).
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Calculate the distance between Points A and B: We will use the distance formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] where \((x_1, y_1)\) are the coordinates of point A and \((x_2, y_2)\) are the coordinates of point B.
Substituting the coordinates:
- \(A(40, 70)\)
- \(B(80, 30)\)
\[ d = \sqrt{(80 - 40)^2 + (30 - 70)^2} \] \[ d = \sqrt{(40)^2 + (-40)^2} \] \[ d = \sqrt{1600 + 1600} \] \[ d = \sqrt{3200} \] \[ d = 40\sqrt{2} \]
Now, we can approximate \(40\sqrt{2}\) since \(\sqrt{2} \approx 1.414\): \[ d \approx 40 \times 1.414 \approx 56.56 \]
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Choose the closest answer: The calculated length of the side between points A and B is approximately \(56.56\) feet. In the list of options provided:
- A. 30 ft
- B. 40 ft
- C. 50 ft
- D. 70 ft
The closest option is C. 50 ft.