Perimeter:
The perimeter of a shape in the coordinate plane is the distance around the shape. To find the perimeter of a shape, you will need to add up the lengths of all the sides of the shape.
For example, let's say we have a rectangle with the following vertices: A(1,2), B(1,5), C(4,5), and D(4,2). To find the perimeter of this rectangle, we need to add up the lengths of all four sides.
Side AB:
Distance = √((1-1)^2 + (5-2)^2) = √(0 + 9) = √9 = 3
Side BC:
Distance = √((4-1)^2 + (5-5)^2) = √(9 + 0) = √9 = 3
Side CD:
Distance = √((4-4)^2 + (2-5)^2) = √(0 + 9) = √9 = 3
Side DA:
Distance = √((1-4)^2 + (2-2)^2) = √(9 + 0) = √9 = 3
Therefore, the perimeter of this rectangle is: 3 + 3 + 3 + 3 = 12
Area:
The area of a shape in the coordinate plane is the amount of space enclosed by the shape. To find the area of a shape, you will need to use various geometric formulas depending on the shape.
For example, to find the area of the rectangle with vertices A(1,2), B(1,5), C(4,5), and D(4,2), we can use the formula for the area of a rectangle:
Area = length * width
To find the length, we can use the distance formula between points A and B or C and D:
Length = Distance between A and B = √((1-1)^2 + (5-2)^2) = 3
To find the width, we can use the distance formula between points A and D or B and C:
Width = Distance between A and D = √((1-4)^2 + (2-2)^2) = 3
Therefore, the area of this rectangle is: 3 * 3 = 9.
6B Math perimeter and area in the coordinate plane
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