Perimeter and area calculations can be done for geometric shapes in the coordinate plane using formulas derived from the coordinates of the points of the shape.
For a rectangle with opposite corners at points (x1, y1) and (x2, y2), the perimeter can be calculated using the formula:
Perimeter = 2 * (|x2 - x1| + |y2 - y1|)
The area of the rectangle can be calculated using the formula:
Area = |x2 - x1| * |y2 - y1|
Similarly, for a triangle with vertices at points (x1, y1), (x2, y2), and (x3, y3), the perimeter can be calculated by summing the lengths of the sides of the triangle:
Perimeter = |x2 - x1| + |x3 - x2| + |x1 - x3| + |y2 - y1| + |y3 - y2| + |y1 - y3|
The area of a triangle can be calculated using the formula for the determinant of a matrix (called the shoelace formula):
Area = 0.5 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
By using these formulas, the perimeter and area of geometric shapes in the coordinate plane can be calculated based on the coordinates of their vertices.
Math perimeter and area in the coordinate plane
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