Find the area of a rectangle ABCD that has vertices point A (1,−4), point B (4,−4), point C (4, 0), and point D (1, 0) in square miles.
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1 point
To find the area of a rectangle, we can use the formula:
Area = length x width
To find the length, we can use the distance formula between points A and B (or points A and D):
Length = √((x2 - x1)^2 + (y2 - y1)^2)
Length = √((4 - 1)^2 + (-4 - (-4))^2)
Length = √(3^2 + 0)
Length = √9
Length = 3 miles
Similarly, the width can be found by using the distance formula between points A and D (or points B and C):
Width = √((x2 - x1)^2 + (y2 - y1)^2)
Width = √((4 - 1)^2 + (0 - (-4))^2)
Width = √(3^2 + 4^2)
Width = √(9 + 16)
Width = √25
Width = 5 miles
Now, we can find the area of the rectangle:
Area = Length x Width
Area = 3 miles x 5 miles
Area = 15 square miles
Therefore, the area of the rectangle ABCD is 15 square miles.