Basic Coordinate Geometry (AQA A Level Maths): Revision Note

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

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

How do I find the midpoint of a line segment?

• 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

How do I find the gradient of a line segment?

• There are lots of ways to find the gradient, m, of a line segment

• Use the two end points to find the change in y divided by change in x