Coordinate Geometry: Distance and Section Formulas Coordinate geometry is a branch of geometry that uses coordinates and geometric shapes to solve problems....
Coordinate Geometry: Distance and Section Formulas
Coordinate geometry is a branch of geometry that uses coordinates and geometric shapes to solve problems. It provides a powerful tool for understanding and analyzing spatial relationships between objects, particularly in two and three dimensions.
Distance Formulas:
Distance between two points (x1, y1) and (x2, y2) is given by the formula: √(x2 - x1)^2 + (y2 - y1)^2.
Distance between a point and the origin is always 0.
Section Formulas:
Area of a triangle with base (b) and height (h) is given by the formula: b * h.
Area of a rectangle with length (l) and width (w) is given by the formula: l * w.
Area of a circle with radius (r) is given by the formula: πr^2.
Area of a sector of a circle with central angle θ is given by the formula: (1/2)θr^2.
Examples:
Area of triangle ABC: 1/2 * 3 * 4 = 6 square units.
Area of rectangle ABCD: 5 * 6 = 30 square units.
Area of circle C with radius r = 2: π(2)^2 = 4π square units.
Area of a sector of a circle with θ = 60 degrees: (1/2) * 60 * 2^2 = 30 square units