The four quadrants

What about points on neither axis? The flat surface holding the axes is called the Cartesian plane (or coordinate plane, or xy-plane). The two axes cut it into four quadrants, numbered I, II, III, IV, going anticlockwise from the top right.

Read the signs to find the quadrant:

• Quadrant I: (+, +)
• Quadrant II: (–, +)
• Quadrant III: (–, –)
• Quadrant IV: (+, –)

What the two numbers mean. For P (x, y):

• x is how far P is from the y-axis (left or right);
• y is how far P is from the x-axis (up or down).

The first number always tells you across, the second tells you up or down.

In Fig. 1.4, S (3, –5) is in Quadrant IV: 3 to the right, 5 down. Q (–5, 3) is in Quadrant II: 5 to the left, 3 up.

A point on an axis is in no quadrant. Every point on the y-axis has x = 0; every point on the x-axis has y = 0.

Order matters, just as in an address. (2, 5) and (5, 2) are different points. (x, y) and (y, x) are the same point only when x = y.