Basic Coordinate Geometry (CIE A Level Maths: Pure 1)

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Basic Coordinate Geometry

What is basic coordinate geometry?

  • Basic coordinate geometry refers to working with points, lines and shapes on the coordinate axis
  • Cartesian coordinates are simply the x -y coordinate system
  • Using coordinates you can
    • Calculate the distance between two points (length of a line)
    • Divide lines in m:n ratio,
    • Find the mid-point of a line
    • Calculate the area of a triangle (or other shapes)
    • Find missing coordinates using any of the above
  • Most of these involve working with straight line graphs
  • Straight line graphs are of the form y = mx + c
    • m is the gradient
    • c is the y-axis intercept
    • Part of a straight line is called a line segment

Basic Coordinate Geometry Notes Diagram 1, A Level & AS Level Pure Maths Revision Notes

 

 

How do I find the length of a line (segment)?

  • By finding the distance, d, between two points (x1, y1) (x2, y2)
  • Pythagoras’ Theorem (a2 = b2 + c2) is used to find the length of a line

 

Basic Coordinate Geometry Notes Diagram 2, A Level & AS Level Pure Maths Revision Notes

 

 

Basic Coordinate Geometry Notes Diagram 3, A Level & AS Level Pure Maths Revision Notes

 

 

Basic Coordinate Geometry Notes Diagram 4, A Level & AS Level Pure Maths Revision Notes

How do I find the midpoint of a line (segment)?

Basic Coordinate Geometry Notes Diagram 5, A Level & AS Level Pure Maths Revision Notes

 

  • M is often used as the midpoint between two points (x1, y1) (x2, y2)
  • It is the average of both the x and y coordinates

Examiner Tip

  • Work with the square of a distance for as long as possible as this avoids early rounding errors and surds.
  • Only square root when forced to or for a final answer, and use the ANS button (and other memory features) on your calculator.

Worked example

Basic Coordinate Geometry Example Diagram, A Level & AS Level Pure Maths Revision Notes

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Paul

Author: Paul

Expertise: Maths

Paul has taught mathematics for 20 years and has been an examiner for Edexcel for over a decade. GCSE, A level, pure, mechanics, statistics, discrete – if it’s in a Maths exam, Paul will know about it. Paul is a passionate fan of clear and colourful notes with fascinating diagrams – one of the many reasons he is excited to be a member of the SME team.