Basic Coordinate Geometry (Edexcel IAL Maths)

Spec point — 2.1

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) and (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) and (x₂, y₂)
• It is the average of both the x and y coordinates

Exam Hint

• 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.

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

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Worked Example