Theory:

  • Co-ordinates are ordered pairs used to represent the position of a point in the cartesian plane.
  • The terms \((x, y)\), \((-x, y)\), \((-x,-y)\), \((x,-y)\) are called co-ordinates which are used to locate the position of a point in the quadrants \(I\), \(II\), \(III\) and \(IV\) respectively in a cartesian plane.
  • \(x\)-co-ordinate of a point:
     
    The \(x\)-coordinate of a point is the perpendicular distance from the \(y\)-axis measured along the \(x\)-axis.
     
    \(y\)-co-ordinate of a point:
     
    The \(y\)-coordinate of a point is the perpendicular distance from the \(x\)-axis measured along the \(y\)-axis.
     
    hf.PNG
      
    1. The perpendicular distance of the point \(L\) from the \(y\)-axis measured along the positive direction of the \(y\)-axis is \(LX=4\) units and the perpendicular distance of the point \(L\) from the \(x\)-axis measured along the positive direction of the \(x\)-axis \(OL=3\) units.
    Point \(L\) lies at the first quadrant in the above graph; hence its co-ordinates will be represented as \((x, y)\), where \(x=3\) and \(y=4\) is the co-ordinate of \(L\) in cartesian plane is represented as \((3,4)\).
     
    2. The perpendicular distance of the point \(M\) from the \(y\)-axis measured along the positive direction of the \(y\)-axis is \(MX'=2\) units and the perpendicular distance of the point \(M\) from the \(x\)-axis measured along the negative direction of the \(x\)-axis \(OM=2\) units.
    Point \(M\) lies at the second quadrant in the above graph; hence its co-ordinates will be represented as \((-x, y)\), where \(x=4\) and \(y=2\) is the co-ordinate of \(M\) in cartesian plane is represented \((-4,2)\).
     
    3. The perpendicular distance of the point \(N\) from the \(y\)-axis measured along the negative direction of the \(y\)-axis is \(NX'=3\) units and the perpendicular distance of the point \(N\) from the \(x\)-axis measured along the negative direction of the \(x\)-axis \(OX'=2\) units.
    Point \(N\) lies at the third quadrant in the above graph; hence its co-ordinates will be represented as \((-x, -y)\), where \(x=2\) and \(y=3\) is the co-ordinate of \(L\) in cartesian plane is represented as \((-2,-3)\).
     
    4. The perpendicular distance of the point \(Q\) from the \(y\)-axis measured along the negative direction of the \(y\)-axis is \(QX=3\) units and the perpendicular distance of the point \(Q\) from the \(x\)-axis measured along the positive direction of the \(x\)-axis \(OX = 1\) unit.
    Point \(Q\) lies at the fourth quadrant in the above graph; hence its co-ordinates will be represented as (x, -y), where \(x=1\) and \(y=3\) is the co-ordinate of \(L\) in cartesian plane is represented as \((1,-3)\). 
    Important!
    Measure the positive coordinate value along the positive direction of the axis and the negative coordinate value along the negative direction of the axis.