Revision Notes: Coordinate Geometry | Mathematics Class 9 ICSE PDF Download

Co-ordinate Geometry is the branch of mathematics in which algebraic methods are used to solve geometrical problems.

Cartesian Plane 

• Two perpendicular number lines intersecting at point zero are called coordinate axes. The horizontal number line is the x-axis (denoted by X’OX) and the vertical one is the y-axis (denoted by Y’OY). The point of intersection of x-axis and y-axis is called origin and denoted by ‘O’. 
• Cartesian plane is a plane obtained by putting the coordinate axes perpendicular to each other in the plane. It is also called coordinate plane or xy plane.
• The x-coordinate of a point is its perpendicular distance from y-axis.
  The y-coordinate of a point is its perpendicular distance from x-axis.
• The point where the x axis and the y axis intersect is represented by coordinate points (0, 0) and is called the origin. 
• The abscissa of a point is the x-coordinate of the point. The ordinate of a point is the y-coordinate of the point. 
• If the abscissa of a point is x and the ordinate of the point is y, then (x, y) are called the coordinates of the point. 
• The axes divide the Cartesian plane into four parts called the quadrants (one fourth part), numbered I, II, III and IV anticlockwise from OX. 
• Sign of coordinates depicts the quadrant in which it lies. 
  
• The coordinates of a point on the x-axis are of the form (x, 0) and that of the point on y-axis are (0, y). 
• To plot a point P (3, 4) in the Cartesian plane, start from origin and count 3 units on the positive x axis then move 4 units towards positive y axis. The point at which we will arrive will be the point P (3, 4). 
  
• If x ≠ y, then (x, y) ≠ (y, x) and if (x, y) = (y, x), then x = y. 

Graphing a Linear Equation

• The Cartesian plane can be used to graph different kinds of situations from everyday life. 
• A line graph which is a whole unbroken line is called a linear graph. 
• Two quantities which vary directly can be plotted as a linear graph. Independent variable is generally taken on x axis the dependent variable is taken on y axis. 
• Steps to draw a graph: 
  (i) Find out the relation between y and x. 
  (ii) Calculate different values of y corresponding to the values of x. 
  (iii) Tabulate the results. 
  (iv) Plot the points. 
  (v) Join the points to obtain the graph. 
• By looking at a linear graph, we can find out the ‘y’ coordinate (or 'x' coordinate) in relation to any point on the ‘x’ axis (or 'y' axis). 
• x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis. 

Inclination and Slope 

• The angle which a straight line makes with the positive direction of the x-axis (measured in the anticlockwise direction) is called inclination of the line. 
  The inclination of the line is usually denoted by θ (theta).  
  In the below figure, θ = 45°
  
• If θ is the inclination of a line then slope of the line is tan θ and is usually denoted by letter m. 
  Slope = m = tan θ. 
  For x-axis and every line parallel to x-axis, the inclination θ = 0°.  
  Hence, Slope (m) = tan θ = tan 0° = 0 
  For y-axis and every line parallel to y-axis, the inclination θ = 90°.  
  Hence, Slope (m) = tan θ = tan 90° = not defined  

Y-Intercept 

• Make y, the subject of the equation. 
  
• The coefficient of x is the slope.
  ⇒ slope (m) = (-a)/b
• The constant term is the y-intercept of the given line. 
  ⇒ y - intercept = (-c)/b