Linear Equations I

Hong Kong

Stage 1 - Stage 3

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

D

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

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