Today is our topic of discussion Coordinate Geometry .
Coordinate Geometry
The portion of geometry where the algebraic expressions of points, straight lines and curved lines are studied is known as the Coordinate Geometry. This portion of geometry is also known as the Analytic Geometry. With the plotting of points on the plane, the straight lines or the curved lines or the figures of the geometric regions made by them such as the triangles, the quadrilaterals, the circles etc. are expressed.
The system of plotting of points on the plane was initiated by a French mathematician named Rene Descates (known as Descartes). The coordinate system of geometry initiated by Descartes is called the Cartesian coordinate system after his name. The coordinate geometry and the analytical geometry are mainly based on Cartesian coordinate system. So, Descates is called the initiator of the analytical geometry.
In the first part of this chapter, the tricks of determining the distance between two points will be discussed through developing the concept of the Cartesian coordinate system among the students.
In the second part, the method of determining the area of any triangle and quadrilateral created by straight lines will be discussed. On the other hand, in the third part, the tricks of determining the slope of a straight line and the simplification of the joining straight line between the two points will be explained. No figure or equation associated with the curved line will be discussed here. In higher classes, it will be discussed elaborately. After completing this chapter, the students will be able to –
- explain the rectangular Cartesian coordinate system;
- find the distance between two points;
- explain the concept of slope (gradient) of a straight line;
- find the equation of a straight line;
- determine the area of a triangle using coordinate system
- find areas of triangular and quadrangular regions by measuring the lengths of the sides;
- construct the geometric figures of the triangles and quadrilaterals by
- plotting of points;
- present an equation of a straight line by plotting points.
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