Coordinate goemetry


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Coordinate goemetry

  1. 1. Coordinate geometry or the system of coordinate geometry has been derived from the correspondence of the points on the number line and real number. A very unique number coordinate can be represented on a number line and any of the real number can be located on the number line. The number line represents the whole of the real number. By the way of the convection the number line is a horizontal placed line at its right hand side the positive Numbers are placed and on the left hand side the negative number are placed and they both are separated by the 0 or we can say zero is placed in the middle of them.
  2. 2. Coordinate system , or Cartesian coordinate system as is sometimes known, is a rectangular system used to uniquely determine a point in two or three dimensional space by its distance from the origin of the coordinate system. It gained its name from a French mathematician and philosopher René Descartes (1596-1650),.The method of describing the location of points in this way was proposed by René Descartes (1596 - 1650). He developed ideas about this system in his book - Discourse on Method(published in 1637He proposed further that curves and lines could be described by equations using this technique, thus being the first to link algebra and geometry.
  3. 3. The coordinate plane is a two-dimensional surface on which we can plot points, lines and curves. It has two scales, called the x-axis and y-axis, at right angles to each other. The plural of axis is 'axes' . Points on the plane are located using two numbers - x and y coordinates. These are the horizontal and vertical distances of the point from a specific location called the origin. Coordinate plane
  4. 4. X axis The horizontal scale is called the x-axis. As you go to the right on the scale from zero, the values are positive and get larger. As you go to the left from zero, they get more and more negative. Y axis The vertical scale is called the y-axis. As you go up from zero the numbers are increasing in a positive direction. As you go down from zero they get more and more negative. Axis labeling Along each axis you will see small tic marks with numbers. These are labels to help judge the scale. They are shown every 5 units in the figure above, but can be any increment, and need not be the same on both axes. Origin The point where the two axes cross (at zero on both scales) is called the origin. The origin is the point from which all distances along the x and y axes are measured. In the figure above you can drag the origin point to reposition it to a more suitable location at any time.
  5. 5. The two axes divide the plane into four areas called quadrants. The first quadrant, by convention, is the top right, and then they go around counter-clockwise. In the diagram above they are labeled Quadrant 1,2 etc. It is conventional to label them with numerals but we talk about them as "first, second, third, and fourth quadrant". They are also sometimes labeled with Roman numerals: I, II, III and IV.
  6. 6. The coordinates of a point are a pair of numbers that define its exact location on a two-dimensional plane. Recall that the coordinate plane has two axes at right angles to each other, called the x and y -axis. The coordinates of a given point represent how far along each axis the point is located.
  7. 7. Ordered Pair The coordinates are written as an "ordered pair" as shown below. The letter P is simply the name of the point and is used to distinguish it from others. The two numbers in parentheses are the x and y coordinate of the point. The first number (x) specifies how far along the x (horizontal) axis the point is. The second is the y coordinate and specifies how far up or down the y axis to go. It is called an ordered pair because the order of the two numbers matters - the first is always the x (horizontal) coordinate. The sign of the coordinate is important. A positive number means to go to the right (x) or up(y). Negative numbers mean to go left (x) or down (y). (The figure at the top of the page has the values of the axes labeled with the appropriate sign). Abscissa The abscissa is another name for the x (horizontal) coordinate of a point. Not used very much. Most commonly, the term "x-coordinate" is used. Ordinate The ordinate is another name for the y (vertical) coordinate of a point. Not used very much. Most commonly, the term "y-coordinate" is used.
  8. 8.  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.