Introduction to Coordinate Geometry

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Coordinate Geometry

Coordinate geometry is a branch of mathematics that deals with the study of geometric figures in a plane using the Cartesian coordinate system. The Cartesian coordinate system, also known as the rectangular coordinate system, was invented by the French mathematician René Descartes in the 17th century.

In the Cartesian coordinate system, every point in the plane is uniquely identified by an ordered pair of numbers (x, y) called its coordinates. The x-coordinate represents the horizontal position of the point, and the y-coordinate represents the vertical position of the point. The origin, denoted by (0, 0), is the point where the x-axis and y-axis intersect.

Coordinate geometry involves using algebraic techniques to solve problems involving points, lines, curves, and other geometric figures in the plane. Some common topics in coordinate geometry include:

Distance Formula: The formula for finding the distance between two points in a plane using their coordinates.

Midpoint Formula: The formula for finding the midpoint between two points in a plane using their coordinates.

Slope of a Line: The formula for finding the slope of a line passing through two points in a plane.

Equation of a Line: The equation of a line passing through a given point with a given slope, or through two given points.

Parallel and Perpendicular Lines: The equations of lines that are parallel or perpendicular to a given line.

Conic Sections: The study of curves obtained by intersecting a plane with a cone, such as circles, ellipses, parabolas, and hyperbolas.

Coordinate geometry is an important tool in many fields, including physics, engineering, computer graphics, and geography.