Coordinate Plane Basics

📍 The Coordinate Plane

Part 1 of 5 — Concept Introduction

Imagine you want to tell a friend exactly where to find a hidden treasure on a map. You could say "go 3 steps right and 2 steps up." That is exactly how the coordinate plane works!

The coordinate plane (also called the Cartesian plane) is made of two number lines that cross each other. Together they form a grid that lets us name the exact location of any point using just two numbers.

The Two Number Lines (Axes)

Axis	Direction	Goes...	Positive side	Negative side
x-axis	Horizontal ↔	Left and right	Right of center	Left of center
y-axis	Vertical ↕	Up and down	Up from center	Down from center

Think of the x-axis as the floor and the y-axis as the wall. Where they cross is your starting spot.

The Origin 🏠

The point where the x-axis and y-axis meet is called the origin. The origin is like "home base" — it is where every trip across the coordinate plane begins.

The origin always has the coordinates $(0, 0)$, because you have not moved left, right, up, or down yet.

Ordered Pairs

We name a location using an ordered pair. It looks like this:

$(x, y)$

• The first number is the x-coordinate (how far left or right).
• The second number is the y-coordinate (how far up or down).

The order matters! Always write x first, then y.

💡 "x comes before y, just like in the alphabet!"

A Worked Example

Let's read the point $(4, 2)$ together.

• The first number is $4$. Since it is positive, move 4 units to the right along the x-axis.
• The second number is $2$. Since it is positive, move 2 units up from there.
• Mark the spot — that is the point $(4, 2)$!

Now look at the point .

Concept Check 🎯

Make sure you remember the order of the numbers in an ordered pair.

📝 Worked Examples

Part 2 of 5 — Plotting Points Step by Step

Follow the same four steps every time you plot a point:

1. Start at the origin $(0, 0)$.
2. Look at the x-coordinate → move right (positive) or left (negative).
3. Look at the y-coordinate → move up (positive) or down (negative).
4. Mark the point where you land.

Example 1: Plot $(5, 3)$

• Start at the origin $(0, 0)$.

🧭 Guided Practice

Part 3 of 5 — Guided Practice

Read each ordered pair carefully and think about the direction of each move.

Fill In the Directions 🔍

Complete the sentences that describe how to plot the point $(-4, 3)$.

🌍 Application & Word Problems

Part 4 of 5 — Real-World Coordinate Plane

The coordinate plane is not just for math class — it shows up everywhere! Video games, treasure maps, seating charts, and even GPS apps use ordered pairs to find locations.

City Grid Example 🗺️

Imagine a city where every street is laid out on a grid. The town hall sits at the origin $(0, 0)$.

To get to the library, you walk 5 blocks east (right) and 2 blocks north (up). On a coordinate plane, east is positive x and north is positive y. So the library is at:

$(5, 2)$

To get to the park, you walk 3 blocks west (left) and 4 blocks north (up). West is negative x, so the park is at:

🏆 Review & Challenge

Part 5 of 5 — Review & Challenge

You made it! Here is everything you learned about the coordinate plane, all in one place.

Quick Summary Table

Term	What It Means	Key Fact
x-axis	Horizontal number line	Right is positive, left is negative
y-axis	Vertical number line	Up is positive, down is negative
Origin	Where the axes cross	Always $(0, 0)$
Ordered pair	A point's location	Written $($ —