Lesson 4.1

The Coordinate Plane

It's the map of algebra. Every point has an address, and every line tells a story. Welcome to the grid.

Introduction

Imagine a city with two main streets: one going Left-Right (X) and one going Up-Down (Y). Where they cross is the center of town, called the Origin. By counting blocks from the center, we can locate anything.

Past Knowledge

Lesson 1.8 (Number Lines). We are just crossing two number lines perpendicular to each other.

Today's Goal

Plot points (x, y), identify Quadrants (I, II, III, IV), and navigate the grid.

Future Success

This is the foundation for ALL graphing: lines, parabolas, and functions.

Key Concepts

Anatomy of the Grid

X
X-Axis (Horizontal)
Left represents negative, Right represents positive.
Y
Y-Axis (Vertical)
Down represents negative, Up represents positive.
O
Origin (0, 0)
The starting point where the axes cross.

Worked Examples

Example 1: Plotting Exact Points

Basic

Plot the point .

Start at Origin

Always start your pencil at (0,0).

Move X (Horizontal)

The first number is 3. Move Right 3.

Move Y (Vertical)

The second number is -4. Move Down 4.

Example 2: Identifying Quadrants

Intermediate

In which quadrant is ?

Negative (-2)

Left side of grid.

Positive (5)

Top side of grid.

Left + Up = Quadrant II

Example 3: Zero Points (Axis Huggers)

Advanced

Plot and .

Point B (0, 3)

X is 0. Don't move left or right! Just go Up 3.

Y-Intercept

Point C (-4, 0)

Y is 0. Don't move up or down! Just go Left 4.

X-Intercept

Common Pitfalls

Mixing X and Y

Remember alphabetical order: X comes before Y. (Left, Right) then (Up, Down). Visualize walking to the elevator (X) before going up (Y).

Zero Confusion

Starting at (0,3) vs (3,0). If the zero is first, you stay on the vertical line (Y-axis). If the zero is second, you stay on the horizontal line (X-axis).

Real-Life Applications

GPS & Maps: Every location on Google Maps is a coordinate (Latitude, Longitude). Latitude is your Y-value (North/South), and Longitude is your X-value (East/West). Your phone is just a very fancy coordinate plane calculator.