Coordinate Geometry (DP IB Analysis & Approaches (AA)) : Revision Note
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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
This is given in the formula booklet under the prior learning section at the beginning

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
This is given in the formula booklet in the prior learning section at the beginning
Pythagoras’ Theorem
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]

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
This is given in the formula booklet under section 2.1 Gradient formula
This is usually known as
Worked Example
Point A has coordinates (3, -4) and point B has coordinates (-5, 2).
i) Calculate the distance of the line segment AB.

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

iii) Find the midpoint of [AB ] .

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