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

The **$y$ y-axis** is the

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.

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...

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

1st quadrant

A2nd quadrant

B3rd quadrant

C4th quadrant

D1st quadrant

A2nd quadrant

B3rd quadrant

C4th quadrant

D

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

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

Relate tables, graphs, and equations to linear and simple quadratic relationships found in number and spatial patterns.

Define and use transformations and describe the invariant properties of figures and objects under these transformations