# 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

*x-axis*. We measure how far

*up*each point on the graph is using the vertical

*y-axis*.

## Dictionary Definition

The Merriam-Webster dictionary defines a graph as "a diagram (such as a series of one or more points, lines, line segments, curves, or areas)."## What Is Coordinate Geometry?

Coordinates are used to describe the position of a point on the graph.-
The
**x-coordinate**measures how far**across**the point is (in the horizontal direction) along the x-axis. In general, if the point is**x**units along the x-axis, its x-coordinate is**x**. -
The
**y-coordinate**measures how far**up**the point is (in the vertical direction) up the y-axis. In general, if the point is**y**units up the y-axis, its y-coordinate is**y**.

The x-coordinate (x) and the y-coordinate (y) are then written in brackets, separated by a comma. The x-coordinate is on the left, the y-coordinate 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.

## The Curriculum

The lessons are grouped into mini-curriculum to help you organise your learning. A brief description is given for each mini-curriculum. Click the**MORE**button to learn more.

## 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 mini-curriculum, 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 mini-curriculum, 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 mini-curriculum, 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 mini-curriculum, 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 mini-curriculum, 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 mini-curriculum, you will learn about the equation of a circle.