The plane and its four parts
Two axes cut the plane into four quadrants.
A sheet that never ends
So far every point we met was on a line. But a floor has places everywhere, not only along two lines. Picture a flat sheet that goes on forever in every direction, with the x-axis and y-axis drawn across it.
The x-axis and the y-axis cross each other. Into how many parts do they cut the sheet?
What this lesson covers
The idea
The plane in which the axes lie is called the Cartesian plane, the coordinate plane or the xy-plane; the axes divide it into four parts called quadrants.
A sheet that never ends
So far every point we met was on a line. But a floor has places everywhere, not only along two lines. Picture a flat sheet that goes on forever in every direction, with the x-axis and y-axis drawn across it.
The x-axis and the y-axis cross each other. Into how many parts do they cut the sheet?
- 2
- 3
- 4
- 6
Cut the sheet
Draw the axes one at a time and see how the sheet is cut.
Quadrants
The plane in which the axes lie is called the Cartesian plane, the coordinate plane or the xy-plane. The axes divide it into four parts called quadrants.
The quadrants are numbered I, II, III, IV, going anticlockwise from the top right. Next you will see what is special about the numbers in each one.
Notes
The Cartesian plane (coordinate plane, xy-plane) is cut by the axes into four quadrants: I, II, III and IV.
Check yourself
How many quadrants does the Cartesian plane have?
Which of these is not another name for the Cartesian plane?
Which quadrant is shaded?
What do the x-axis and y-axis together do to the plane?
- 2. One axis alone makes two halves. Both axes together make more parts.
- 3. The two axes cut the plane into four parts, not three.
- 4 — correct. Yes. The two axes divide the plane into four quadrants.
- 8. There are four parts: the two axes cut the plane just twice.
- The coordinate plane. This is another name for the Cartesian plane.
- The xy-plane. This is another name for the Cartesian plane.
- The number line — correct. Right. The number line is one-dimensional: only one line. The plane has two axes.
- I. Quadrant I is the top-right part.
- II — correct. Yes. Quadrant II is next, going anticlockwise: the top-left part.
- III. Quadrant III is the bottom-left part.
- IV. Quadrant IV is the bottom-right part.
- Cut it into four quadrants — correct. Yes. Two axes, four quadrants.
- Cut it into two halves only. One axis alone gives two halves. With both axes the plane has four parts.
- Turn it into a number line. A number line has one axis. The plane keeps both axes and is cut into four parts.