4-5 The Coordinate Plane

Property

A coordinate plane is a grid formed by a horizontal x-axis and a vertical y-axis that meet at the origin $(0,0)$. Points are located using ordered pairs $(x,y)$, where the x-coordinate is the horizontal position and the y-coordinate is the vertical position.

Examples

To plot $(5, 3)$, start at the origin $(0,0)$, move 5 units right, then 3 units up.
To plot $(-2, 1)$, start at the origin, move 2 units left, then 1 unit up.
To plot $(-4, -6)$, start at the origin, move 4 units left, then 6 units down.

Explanation

Think of it as a treasure map where 'X' marks the spot at the origin! The first number in an ordered pair, $(x,y)$, tells you how many steps to take left or right. The second number tells you how many steps to go up or down to find your point!

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