Use Coordinate Geometry to Solve Problems Quick Check
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Question
Apply the techniques of using the coordinates to find the length and the width of the polygon. Use the length and the width to find the perimeter of the polygon in miles. Rectangle ABCD has vertices point A (1,−3) , point B (5, −3) , point C (5, −1) , and point D (1, −1) .(1 point)
Responses
8 square miles
8 square miles
−12 miles
negative 12 miles
12 miles
12 miles
12 square miles
12 square miles
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To find the length of the rectangle, we can use the distance formula:
Length = √((x2 - x1)^2 + (y2 - y1)^2)
Length = √((5 - 1)^2 + (-3 -(-3))^2)
Length = √(4^2 + 0^2)
Length = √(16)
Length = 4 miles
To find the width of the rectangle, we can use the same formula:
Width = √((x4 - x1)^2 + (y4 - y1)^2)
Width = √((1 - 1)^2 + (-1 -(-3))^2)
Width = √(0^2 + 2^2)
Width = √(4)
Width = 2 miles
To find the perimeter, we add up the lengths of all sides:
Perimeter = 2(Length + Width)
Perimeter = 2(4 + 2)
Perimeter = 2(6)
Perimeter = 12 miles
Therefore, the perimeter of the rectangle ABCD is 12 miles.