Lesson 5: The Coordinate Plane

Property

The Standard Coordinatization of the Plane
Draw a horizontal line and a vertical line, so that the point of intersection is center page. That point is called the origin and is denoted $(0,0)$.
Decide which variable is to be measured along the horizontal line ($x$), and which is measured along the vertical line ($y$).
Select a measure to represent a unit on both axes. Now, $(x, y)$ is found by moving $x$ units on the horizontal axis, and then $y$ units in the vertical direction.

Examples

• To plot the point $(2, 5)$, start at the origin $(0,0)$, move 2 units to the right, and then 5 units up. This point is in Quadrant 1.
• The point $(-4, -1)$ is found by moving 4 units to the left from the origin and then 1 unit down. This point is in Quadrant 3.
• A point with a zero coordinate lies on an axis. The point $(0, 3)$ is on the y-axis, and the point $(-5, 0)$ is on the x-axis.

Explanation

The coordinate plane is like a map made from two number lines (axes) that cross at a right angle. The point $(x, y)$ tells you how far to move horizontally (x-value) and then vertically (y-value) from the start (origin).

Property

The coordinate plane is divided into four quadrants labeled with Roman numerals:

• Quadrant I: $(+,+)$ both coordinates positive
• Quadrant II: $(-,+)$ x negative, y positive
• Quadrant III: $(-,-)$ both coordinates negative
• Quadrant IV: $(+,-)$ x positive, y negative

Examples

Property

Points that lie on the x-axis or y-axis are not located in any quadrant.
A point $(a, 0)$ lies on the x-axis, and a point $(0, b)$ lies on the y-axis.

Examples