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Quadrants

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Quadrants

Study Guide

Key Definition

The Cartesian plane is divided into four quadrants. In Quadrant I, both the $x$ and $y$ coordinates are positive.

Important Notes

Quadrants are numbered I through IV, counterclockwise starting from the upper right.
In Quadrant II, the $x$ is negative and $y$ is positive.
In Quadrant III, both $x$ and $y$ are negative.
In Quadrant IV, $x$ is positive and $y$ is negative.
Points on the axes are not in any quadrant.

Mathematical Notation

$(x, y)$ denotes a point in the Cartesian plane

$x > 0$ indicates x is positive

$y < 0$ indicates y is negative

$±$ indicates positive or negative

Remember to use proper notation when solving problems

Why It Works

Understanding quadrants helps in graphing points and solving geometric problems on the Cartesian plane using $(x, y)$ coordinates.

Remember

Quadrants help determine the signs of coordinates in $(x, y)$ pairs.

Quick Reference

Quadrant I:$x > 0, y > 0$

Quadrant II:$x < 0, y > 0$

Quadrant III:$x < 0, y < 0$

Quadrant IV:$x > 0, y < 0$

Understanding Quadrants

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Quadrants divide the Cartesian plane into four regions using the x- and y-axes.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which quadrant contains the point $(3, 4)$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

A teenager is locating a friend using coordinates $(-5, 6)$. Which quadrant are they in?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Determine the quadrant for the point $(-7, -3)$.

Challenge Quiz

Single Choice Quiz

Advanced

If a point lies on the line $y = -x$, which quadrants could it be in?

Recap

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Review key concepts and takeaways