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The Number Plane


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).

Loading Graph...


Question 2


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

  1. 1st quadrant


    2nd quadrant


    3rd quadrant


    4th quadrant


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 $=$=$\left(\editable{},\editable{}\right)$(,)


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