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To find the area of the parallelogram formed by connecting the points A(4,-3), B(-2,-3), C(-1,1), and D(5,1), you can follow these steps:
1. Find the distance between points A and B (base of the parallelogram):
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((-2 - 4)^2 + (-3 - (-3))^2)
Distance = √((-6)^2 + (0)^2)
Distance = √(36 + 0)
Distance = √36
Distance = 6 units
2. Find the height of the parallelogram (distance between lines AB and CD):
Height = Absolute difference in y-coordinates of points C and D
Height = |1 - (-3)|
Height = |1 + 3|
Height = 4 units
3. Calculate the area of the parallelogram:
Area = Base x Height
Area = 6 units x 4 units
Area = 24 square units
Therefore, the correct area of the parallelogram formed by the given points A, B, C, and D is 24 square units, not 18 square units as stated in the previous answer.
