Graphs and Coordinate Geometry (Mathematics Curriculum)
What Is a Graph?
A graph is a diagram that allows us to draw points, lines, curves and other shapes.
A graph uses a pair of axes at right angles to each other: one horizontal and one vertical.
We measure how far across each point on the graph is using the horizontal xaxis. We measure how far up each point on the graph is using the vertical yaxis.
Dictionary Definition
The MerriamWebster dictionary defines a graph as "a diagram (such as a series of one or more points, lines, line segments, curves, or areas)."
A graph is shown below:
What Is Coordinate Geometry?
Coordinates are used to describe the position of a point on the graph.

The xcoordinate measures how far across the point is (in the horizontal direction) along the xaxis.
In general, if the point is x units along the xaxis, its xcoordinate is x.

The ycoordinate measures how far up the point is (in the vertical direction) up the yaxis.
In general, if the point is y units up the yaxis, its ycoordinate is y.
Each point can be written as a pair of coordinates:
The xcoordinate (x) and the ycoordinate (y) are then written in brackets, separated by a comma. The xcoordinate is on the left, the ycoordinate is on the right.
The coordinates can be used to describe points on lines, curves and shapes. This is coordinate geometry.
Here are some examples from coordinate geometry. We might be interested in the distance between two points. We might want be interested in how a shape is moved. Coordinate geometry allows us to do this.
Graphs
A graph is a diagram that allows us to draw points, lines, curves and other shapes.
A graph uses a pair of axes at right angles to each other: one horizontal and one vertical.
In this minicurriculum, you will learn about the parts of a graph.
Cartesian Coordinates
Cartesian coordinates are used to describe the position of a point on a graph.
In this minicurriculum, you will learn about Cartesian coordinates and how they are used to describe and draw points.
Polar Coordinates
Polar coordinates are another coordinate system. They are used to describe the position of a point on a graph.
In this minicurriculum, you will learn about polar coordinates.
Coordinate Geometry of Points and Lines
Coordinate geometry can be used for points and lines that join any two points.
In this minicurriculum, you will learn about finding the distance and slope between two points and finding the midpoint between two points.
Transformations in Coordinate Geometry
A transformation is a change of a shape. It can change a shape's position, orientation and its size.
Cartesian coordinates can be used to transform a shape.
In this minicurriculum, you will learn about how to use coordinate geometry to move and flip shapes.
Equation of a Circle
A circle can be represented with an equation.
The Cartesian coordinates of the points on the circle satisfy this equation.
In this minicurriculum, you will learn about the equation of a circle.