Location of a point in a plane
The 17th century mathematician Rene Descartes, it is said, noticed the movement of an insect near a corner of the ceiling and began to think of determining the position of a given point in a plane. His system of fixing a point with the help of two measurements, vertical and horizontal, came to be known as Cartesian system, in his honour.
Suppose we want find the location of any point A in a plane.
If the distance between left edge & A is 90 cm, we can say that location of A is 90 cm from the left edge. But there can be many points like A1, A2 which are 90 cm from the left edge. Let the distance between A & bottom edge is 120 cm. Now the location of point A can be described as 90 cm from the left edge and 160 cm from the bottom edge which is unique for A in the given plane & hence complete. It is written as (90, 160). No other point would have the same location.
↪ System designed to define the position of a point on the plane or in space is called coordinate system.
↪ An ordered set of numbers that defines the position of a point on a plane or in space is called coordinates of that point. If the point is on a plane, then ordered set of two numbers (Ordered Pair) are used, each of which represents a distance along an axis, measured from the origin.
↪ One dimensional coordinate system – Number line
↪ Two dimensional coordinate system – It consists of two perpendicular axes (the x-axis or abscissa, and the y-axis or ordinate), marked with measurements of suitable scale, forming a grid . The point of intersection, where the axes meet, is called the origin normally labeled O.
Applications – Cost-quantity graph, Position-time graph, Velocity-time graph,
↪ The perpendicular distance of a point from the y – axis is called its x-coordinate (also called the abscissa).
↪ The perpendicular distance of a point from the x – axis is called its y – coordinate (also called the ordinate).
↪ The Coordinates of a point is stated in the form (x,y), an ordered pair in which the x – coordinate comes first, and then the y – coordinate .
↪ Cartesian coordinate system – Unit & scale of measurement on both axis are same.
Application – Vector operations (addition, subtraction etc.). (Physical quantities having both magnitude & direction are called vectors).