X, Y axes

Background

With a number line, we can look at all the real numbers in a row. But what if I want to draw a shape or otherwise put things in a grid?

Question

Describe a method of laying out a shape on a grid that can be described mathematically.

Answer

Use a two-dimensional grid (in essence, use two number lines)

Analysis

We've started covering topics where having the ability to describe shapes in a manner such that a reader can repeat what a writer has described. And one way to describe points, lines, and other shapes, is to use a grid of perpendicular lines. We can build it this way:

First let's show the number line:



We can set up another number line perpendicular to the first one, running through the number 0:



These are called the axes. The horizontal one (the first one that runs left to right) we can call the "x axis" and the one that runs up and down is called the "y axis".

We can run parallel lines to each axis and in essence create little grids:



And now using these grids we can plot points.

The way we plot points is to use a format of the x value first (going left/right) and then the y value (going up down). We put the numbers into a bracket for easy reading. So for instance we can plot the number (0,0) (it's in blue):



we can plot (4,1):



And we can plot (-1,-2):



We can describe the format as (x,y).

Vocabulary used:

For more information check out these links (comment to add your favourite link):

Where might you have come from?

Fact-orials Index

Numbers:

• Variables

Graphing:

• Number Line

Geometry:

• Intersecting, Parallel, Perpendicular Lines
• Defining a Circle and Right Triangles

Where might we go?