Lesson 11: Investigation 1: The Coordinate Plane

New Concept

Welcome to Math Course 1! This course connects arithmetic to geometry and algebra, showing how numbers can describe relationships and locations on a plane.

What’s next

To begin, we'll explore the coordinate plane—a key tool for visualizing math. Soon, you’ll analyze worked examples on plotting points and calculating area.

Property

Two perpendicular number lines form a coordinate plane. The horizontal number line is called the x-axis. The vertical number line is called the y-axis. The point at which the x-axis and the y-axis intersect (cross) is called the origin.

Examples

The origin is the starting point for all coordinates, located at $(0, 0)$.
The x-axis is the horizontal line where all y-coordinates are $0$.
The y-axis is the vertical line where all x-coordinates are $0$.

Explanation

Think of the coordinate plane as a treasure map for math! The x-axis is your east-west line, the y-axis is your north-south line, and the origin $(0, 0)$ is where X marks the spot. These axes give every single point its own unique address on the map.

Property

The two axes divide the plane into four regions called quadrants, which are numbered counterclockwise beginning with the upper right as first, second, third, and fourth.

Examples

Quadrant I contains points with positive coordinates, like $(+, +)$. For example: $(5, 2)$.
Quadrant II contains points with negative x and positive y coordinates, like $(-, +)$. For example: $(-3, 4)$.
Quadrant III contains points with negative coordinates, like $(-, -)$. For example: $(-1, -6)$.
Quadrant IV contains points with positive x and negative y coordinates, like $(+, -)$. For example: $(7, -2)$.

Explanation

The axes slice the plane into four zones called quadrants! Numbered counterclockwise from the top right, each has a unique sign pattern for its $(x, y)$ coordinates. This pattern is a quick clue to a point's location without even needing to graph it, telling you which corner of the map to look in.

Property

We can identify any point on the coordinate plane with two numbers called coordinates of the point. The coordinates are written as a pair of numbers in parentheses, such as $(3, 2)$.

Examples

To plot the point $(5, 3)$, you start at the origin, move 5 units right, and then 3 units up.
To plot the point $(-2, -4)$, you start at the origin, move 2 units left, and then 4 units down.
A point on the x-axis, like $(4, 0)$, means you move 4 units right but $0$ units up or down.

Explanation

Coordinates are a point's secret address, written as $(x, y)$. The first number tells you how far to 'run' along the x-axis hallway (left or right). The second number tells you how high to 'rise' on the y-axis elevator (up or down). Just remember to run before you rise!