Coordinate Geometry | O Level Mathematics 4024 & IGCSE Mathematics 0580 | Detailed Free Notes To Score An A Star (A*)

Basic Formulae

• For the equation of a line, we use y= mx+c
  • y here represents the variable that is dependent. It depends on the value of x.
    • A dependent variable is always plotted on the vertical axis
    • REMEMBER
      • It is not a MUST that the vertical axis variable will always be named y.
      • It can be named anything.
      • The name of the axis, however, remains the same.
    • x here represents the independent variable. It is the variable the user manipulates
      • An independent variable is always plotted on the X axis
      • REMEMBER
        • It is not MUST that the horizontal axis variable will always be named x.
        • It can be named anything.
        • The name of the axis, however, remains the same.
      • m is the gradient
        • The slope of the line
        • How straight or slant the line is.
        • It is found by simply
          • 
          • In other words, you can also say rise over run
          • The formula will be
            • If two coordinates you select are as follows (x1, y1) and (x2, y2)
            • Then
            • 
            • Remember, you can select any point of the two points as y2, just make sure you select its corresponding x as x2.
          • Gradient of a straight line is the same at all points
            • Why?
            • Because straight line rises without breaking
          • C represents the constant
            • It can also be called the Y-intercept of the equation
            • Y-Intercept
              • The point at which a line will cut the y-axis
              • It will be zero if the y-axis is cut at a perfect zero.
            • Otherwise, once you have the values of m, you will insert one of the points you selected, either (x1,y1) or (x2,y2) in the places of y=mx+c in the equation.
              • Then solve it to get the value of c.
              • C can be negative, it can be positive.

Some Crucial Information To Note

• If two lines are parallel
  • They will have the same gradient, i.e the value of m if the equation is in the form of y=mx+c (do check for anything with y or x).
  • The gradient will have the same sign as well.
• If two lines are perpendicular
  • When you multiply their gradients, you will get minus 1
  • So
    • If m1 is the gradient of line 1
    • and m2 is the gradient of line 2
    • And they are perpendicular
    • Then
      • m1 x m2 = -1
    • If two lines are perpendicular bisector
      • The place where they intersect will cut the line into two EQUAL halves
      • The angle would be 90 degrees
    • If a line bisects another line
      • It passes through the midpoint of the other line
      • If line a bisects line b
      • Line a passes through the midpoint of line b
    • If a line is perpendicular to another line
      • You can use it to find the gradient of the other line using the above mentioned formula
    • Mid-point
      • The exact half of a line
      • Method
        • Take the two farthest points on a line segment
          • Like dono konay walay points
        • Then
        • 
      • If you have to find the midpoint between two points
        • Use those two points in the same equation
      • Distance between two points
        • Simple formula
        • Use those two points
        • And insert in this formula
        •