Coordinate Geometry

Coordinate Geometry

1. 1. Introduction to Coordinate Geometry

   • 1. Cartesian Coordinate System
     • Introduction of terms like Axes, Origin, Abscissa, Ordinate, Ordered pair (x,y), Cartesian Co-ordinate plane. Sign Conventions,Quadarants. Location of a point in four cartesian quadrants and both axes. Plotting of a given point in the Cartesian plane.
   • 2. Representation of Lines and Polygons
     • Points on a line. Plotting line in graph by joining points. Point of Intersections. Representing Polygons.

2. 2. Distance between Points

   • 1. Distance Formula
     • Simple distances. Distance between two points in a coordinate plane. Properties of Various types of Quadrilaterals. Test for Collinearity of three points.
   • 3. Area of Polygons
     • Area of triangle. Condition for Collinearity of three points. Area of Quadrilateral.
   • 2. Section Formula
     • Point of internal division of a line Midpoint formula; Internal and external division in ratio of m:n. Point of trisection. Application to Geometry. Basic terms related to Triangle like, Coordinates of Centroid etc.

3. 3. Slope of Line

   • 1. Concept and Properties of slope
     • Meaning of slope/Gradient of a line. Inference from slope. Meaning of slope = 1. Gradient of a line as a ratio of ‘rise over run’. Negative, zero and positive slopes. Constant slope and Changing slope Slopes of parallel lines and perpendicular lines. Intercepts of a straight line.
   • 2. Computation of slope
     • Computing Slope when: Given equation of a line Slope of line passing through two points. tan (angle)

4. 4.Equation of straight lines

   • 1. Equations of Line
     • Equation of some standard lines: X axis, Y axis, Line parallel to X axis and Y axis. Equation of a line in general form. Slope intercept form of line: y=mx+c. Equation of line passing through origin. Point Slope form: y-y1=m(x-x1). Two point form. Intercept form. Equation of parallel line to given line. Equation of perpendicular line to given line.Ploting line on graph when Equation is given.