IBMaths: AA SLDPRevision Notes3. Geometry & Trigonometry3.1 Geometry Toolkit3.1.1 Coordinate Geometry

Coordinate Geometry (DP IB Maths: AA SL)

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Basic Coordinate Geometry

What are cartesian coordinates?

  • Cartesian coordinates are basically the x-y coordinate system
    • They allow us to label where things are in a two-dimensional plane
  • In the 2D cartesian system, the horizontal axis is labelled x and the vertical axis is labelled y

 

What can we do with coordinates?

  • If we have two points with coordinates (x1 , y1) and (x2 , y2) then we should be able to find
    • The midpoint of the two points
    • The distance between the two points
    • The gradient of the line between them

 

How do I find the midpoint of two points?

  • The midpoint is the average (middle) point
    • It can be found by finding the middle of the x-coordinates and the middle of the y-coordinates
  • The coordinates of the midpoint will be

begin mathsize 22px style open parentheses fraction numerator x subscript 1 plus blank x subscript 2 over denominator 2 end fraction blank comma blank fraction numerator y subscript 1 plus blank y subscript 2 over denominator 2 end fraction blank close parentheses end style

    • This is given in the formula booklet under the prior learning section at the beginning

Basic Coordinate Geometry Notes Diagram 5

How do I find the distance between two points?

  • The distance between two points with coordinates (x1 , y1) and (x2 , y2) can be found using the formula

begin mathsize 22px style d space equals blank square root of open parentheses x subscript 1 minus blank x subscript 2 close parentheses squared space plus space open parentheses y subscript 1 minus blank y subscript 2 close parentheses squared end root blank end style

    • This is given in the formula booklet in the prior learning section at the beginning
  • Pythagoras’ Theorem a squared space equals space b squared plus c squared  is used to find the length of a line between two coordinates
  • If the coordinates are labelled A and B then the line segment between them is written with the notation [AB]

Basic Coordinate Geometry Notes Diagram 2

How do I find the gradient of the line between two points?

  • The gradient of a line between two points with coordinates (x1 , y1) and (x2 , y2) can be found using the formula

begin mathsize 22px style m equals blank fraction numerator y subscript 2 minus blank y subscript 1 over denominator x subscript 2 minus blank x subscript 1 end fraction end style

    • This is given in the formula booklet under section 2.1 Gradient formula
    • This is usually known as  m equals rise over run

Worked example

Point A has coordinates (3, -4) and point B has coordinates (-5, 2).

i)
Calculate the distance of the line segment AB.

ai-sl-3-1-1-basic-cg-we-i

ii)
Find the gradient of the line connecting points A and B.

 ai-sl-3-1-1-basic-cg-we-ii

iii)
Find the midpoint of [AB ] .

ai-sl-3-1-1-basic-cg-we-iii

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Amber

Author: Amber

Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.