Analytic geometry is a branch of mathematics that combines algebra and geometry to study geometric shapes and their properties using coordinates. It was developed by the French mathematician René Descartes in the 17th century.
Coordinates are a set of numbers that specify the position of a point or object on a graph or in a plane. In analytic geometry, coordinates are typically represented by two numbers, x and y, which correspond to the horizontal and vertical axes, respectively.
To find the coordinates of a point on a graph, you can use the point's location relative to the x and y axes. The x-coordinate is the distance from the point to the y-axis, and the y-coordinate is the distance from the point to the x-axis. You can also use the distance formula or Pythagorean theorem to find the coordinates of a point.
The distance formula is a mathematical equation used to find the distance between two points on a graph. It is written as d = √((x2-x1)² + (y2-y1)²), where (x1, y1) and (x2, y2) are the coordinates of the two points. This formula is derived from the Pythagorean theorem.
Analytic geometry has many real-world applications, including in engineering, architecture, and physics. It can be used to design buildings, create computer graphics, and analyze motion and forces. It is also used in navigation systems, such as GPS, to determine the coordinates of locations on Earth.