Introduction to Coordinate Geometry - Math Open Reference (original) (raw)

| | | Introduction to Coordinate Geometry A system of geometry where the position of pointson the planeis described using an ordered pair of numbers. Recall that a plane is a flat surface that goes on forever in both directions. If we were to place a point on the plane, coordinate geometry gives us a way to describe exactly where it is by using two numbers. What are coordinates? To introduce the idea, consider the grid on the right. The columns of the grid are lettered A,B,C etc. The rows are numbered 1,2,3 etc from the top. We can see that the X is in box D3; that is, column D, row 3. D and 3 are called the coordinates of the box. It has two parts: the row and the column. There are many boxes in each row and many boxes in each column. But by having both we can find one single box, where the row and column intersect. The Coordinate Plane In coordinate geometry, points are placed on the "coordinate plane" as shown below. It has two scales - one running across the plane called the "x axis" and another a right angles to it called the y axis. (These can be thought of as similar to the column and row in the paragraph above.) The point where the axes cross is called the origin and is where both x and y are zero. On the x-axis, values to the right are positive and those to the left are negative.On the y-axis, values above the origin are positive and those below are negative. A point's location on the plane is given by two numbers,the first tells where it is on the x-axis and the second which tells where it is on the y-axis. Together, they define a single, unique position on the plane. So in the diagram above, the point A has an x value of 20 and a y value of 15. These are the coordinates of the point A, sometimes referred to as its "rectangular coordinates". Note that the order is important; the x coordinate is always the first one of the pair. For a more in-depth explanation of the coordinate plane see The Coordinate Plane.For more on the coordinates of a point see Coordinates of a Point Things you can do in Coordinate Geometry If you know the coordinates of a group of points you can: Determine the distance between them Find the midpoint, slope and equation of a line segment Determine if lines are parallel or perpendicular Find the area and perimeter of a polygon defined by the points Transform a shape by moving, rotating and reflecting it. Define the equations of curves, circles and ellipses. Information on all these and more can be found in the pages listed below.HistoryThe method of describing the location of points in this way was proposed by the French mathematician René Descartes (1596 - 1650). (Pronounced "day CART"). He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry. In honor of his work, the coordinates of a point are often referred to as its Cartesian coordinates, and the coordinate plane as the Cartesian Coordinate Plane. Other Coordinate Geometry topics Introduction to coordinate geometry The coordinate plane The origin of the plane Axis definition Coordinates of a point Distance between two points Introduction to Lines in Coordinate Geometry Line (Coordinate Geometry) Ray (Coordinate Geometry) Segment (Coordinate Geometry) Midpoint Theorem Distance from a point to a line - When line is horizontal or vertical - Using two line equations - Using trigonometry - Using a formula Intersecting lines Cirumscribed rectangle (bounding box) Area of a triangle (formula method) Area of a triangle (box method) Centroid of a triangle Incenter of a triangle Area of a polygon Algorithm to find the area of a polygon Area of a polygon (calculator) Rectangle Definition and properties, diagonals Area and perimeter Square Definition and properties, diagonals Area and perimeter Trapezoid Definition and properties, altitude, median Area and perimeter Parallelogram Definition and properties, altitude, diagonals Print blank graph paper (C) 2011 Copyright Math Open Reference. 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