# Analytic Geometry - Historical Development Of Analytic Geometry, Cartesian Coordinate System, Distance Between Two Points, Algebraic Equations Of Lines

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geometric real figures

Analytic **geometry** is a branch of **mathematics** that uses algebraic equations to describe the size and position of geometric figures on a coordinate system. Developed during the seventeenth century, it is also known as Cartesian geometry or coordinate geometry. The use of a coordinate system to relate geometric points to **real numbers** is the central idea of analytic geometry. By defining each **point** with a unique set of real numbers, geometric figures such as lines, circles, and conics can be described with algebraic equations. Analytic geometry has found important applications in science and industry alike.

## Additional Topics

During the seventeenth century, finding the solution to problems involving curves became important to industry and science. In astronomy, the slow acceptance of the heliocentric theory (Sun-centered theory) of planetary motion required mathematical formulas that would predict elliptical orbits. Other areas such as optics, navigation, and the military required formulas for things such as determinin…

The link between algebra and geometry was made possible by the development of a coordinate system which allowed geometric ideas, such as point and line, to be described in algebraic terms like real numbers and equations. In the system developed by Descartes, called the rectangular cartesian coordinate system, points on a geometric plane are associated with an ordered pair of real numbers known as …

In addition to length, it is often desirable to find the coordinates of the midpoint of a line segment. These coordinates can be determined by taking the average of the x and y coordinates of each point. For example, the coordinates for the midpoint M (x,y) between points P (2,5) and Q (4,3) are x = (2 + 4)/2 = 3 and y = (5 + 3)/2 = 4. …

One of the most important aspects of analytic geometry is the idea that an algebraic equation can relate to a geometric figure. Consider the equation 2x + 3y = 44. The solution to this equation is an ordered pair (x,y) which represents a point. If the set of every point that makes the equation true (called the locus) were plotted, the resulting graph would be a straight line. For this reason, equa…

One of the most frequent activities in geometry is determining the area of a polygon such as a triangle or square. By using coordinates to represent the vertices, the areas of any polygon can be determined. The area of triangle OPQ, where O lies at (0,0), P at (a,b), and Q at (c,d), is found by first calculating the area of the entire rectangle and subtracting the areas of the three right triangle…

The circle is one kind of a broader type of geometric figures known as conic sections. Conic sections are formed by the intersection of a geometric plane and a double-napped cone. After the circle, the most common conics are parabolas, ellipses, and hyperbolas. Curves known as parabolas are found all around us. For example, they are the shape formed by the sagging of telephone wires or the path a …

Geometric figures such as points, lines, and conics are two-dimensional because they are confined to a single plane. The term two-dimensional is used because each point in this plane is represented by two real numbers. Other geometric shapes like spheres and cubes do not exist in a single plane. These shapes, called surfaces, require a third dimension to describe their location in space. To create…

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## User Comments

over 5 years ago

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over 5 years ago

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over 6 years ago

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