Hong Kong
Stage 1 - Stage 3

# The Number Plane

Lesson

In mathematics, a plane is not something we see zooming around in the sky.  It is a flat 2D surface.  The top of your desk could be a plane, as could your wall or your roof.   A number plane is created by two perpendicular lines that we call an x-axis and a y-axis.

The $x$x-axis is the horizontal line.

The $y$y-axis is the vertical line.

Where the two axes cross each other is labelled the ORIGIN.  It has a zero value on both axes.

The $x$x-axis is numbered with positive numbers increasing to the right.

The $y$y-axis is numbered with positive numbers increasing vertically.

We can notice 2 things from the number plane we have created here:

• The lines have created four distinct sections.  We call these QUADRANTS.  Labeling them anticlockwise from the top right corner.

• We can create a grid from the $2$2 number lines. When labeling points on the grid, we always use the $x$x-value first.

So what sort of things do we need to be able to do with number planes?

• graph points in any quadrant
• read points off a number plane
• find horizontal and vertical distances between points
• solve problems using the coordinate plane.

Let's have a look at these worked examples.

##### Question 1

What are the coordinates of the point shown in the number plane?

Give the coordinates in the form $\left(x,y\right)$(x,y).

##### Question 2

In which quadrant does the point $\left(4,4\right)$(4,4) lie?

A

B

C

D

##### Question 3

Write the coordinates of the point that is $5$5 units to the right of $\left(-3,-4\right)$(3,4).

1. Coordinates $=$=$\left(\editable{},\editable{}\right)$(,)