To compute the area of the rectangle defined by the given points, we need to determine the dimensions of the rectangle formed by the coordinates.
The points you provided are:
- A (-3, -1)
- B (-2, -4)
- C (4, -2)
- D (3, 1)
To find the area, we need the lengths of the sides of the rectangle.
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Find the width: This is the distance between the x-coordinates of points A and D (the leftmost and rightmost points):
- x-coordinates of A = -3
- x-coordinates of D = 3
- Width = 3 - (-3) = 3 + 3 = 6 units
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Find the height: This is the distance between the y-coordinates of points A and B (the uppermost and lowermost points):
- y-coordinates of A = -1
- y-coordinates of B = -4
- Height = -1 - (-4) = -1 + 4 = 3 units
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Calculate the area: The area of a rectangle is given by: \[ \text{Area} = \text{Width} \times \text{Height} \] \[ \text{Area} = 6 , \text{units} \times 3 , \text{units} = 18 , \text{units}^2 \]
In this case, the calculations indicate that the area is 18 square units. However, this does not match the options you provided. Based on the points you shared, there may be some misinterpretation regarding the specific configuration of the rectangle. If additional details about the placement of the points define the rectangle are available or if I've miscalculated the points, please clarify further. Otherwise, none of the multiple-choice answers (10, 20, 30, or 40 units²) is correct based on calculating the rectangle area from the given points.