position

The horizon is a "straight line" where the earth or water meets the sky.

A horizontal line is a line that runs left to right and is parallel to the horizon. A vertical line is a line that runs up and down. 

A vertical line is 90 degrees (perpendicular) to a horizontal line. 

A horizontal and vertical line are both examples of one dimension (1D).

A dimension is being able to measure something in one direction (eg horizontally or vertically, etc)

An axis is a line used to mark numbers or measurements.

The x-axis is a line with numbers, that runs horizontally. It is used to solve problems in one dimension (1D).

The y-axis is a line with numbers, that runs vertically. It is also used to solve problems in one dimension (1D).

If the x-axis and y-axis are combined, we get a set of axes called the Cartesian Plane. This is used to solve problems in two dimensions (2D). The x-axis becomes the first dimension and the y-axis becomes the second dimension. 

The point where the two axes meet is called the origin.

The Cartesian Plane is used to identfy position or location in 2D. We use coordinates to do this by placing two numbers inside a set of brackets, separated by a comma. The x-coordinate comes first, followed by the y-coordinate second.

eg Point J has the coordinate (6, 2)

It is 6 squares horizontally from the origin in the positive direction and 2 squares above the origin

eg Point L has the coordinate (-5, 3)

It is 5 squares horizontally from the origin in the negative direction and 3 squares above the origin

eg Point M has the coordinate (0, -3)

It is 0 squares horizontally from the origin and 3 squares below the origin

The Cartesian Plane is spilt up into 4 sections called quadrants. 

• If we are solving problems in the section where x and y are both positive, we are working in Quadrant 1. 

• If we are solving problems in the section where x is negative but y is positive, we are working in Quadrant 2. 

• If we are solving problems in the section where x and y are both negative, we are working in Quadrant 3. 

• If we are solving problems in the section where x is positive but y is negative, we are working in Quadrant 4. 

Note: We can solve problems in multiple quadrants at once.

In three dimensional (3D) problems, we introduce a z-axis. 

The coordinates would then become (x, y, z)

eg (2, 3, -1) means 2 squares in the positive x direction, 3 squares in positive y direction and 1 square in the negative z direction.