# Ordered Pairs on the Coordinate Plane

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Team Digital
Ordered Pairs on the Coordinate Plane
CCSS.MATH.CONTENT.6.NS.C.6.B

## Ordered Pairs – Introduction

When you think about finding a location, you probably think of a map. In mathematics, we use a similar concept to find locations, but we call them ordered pairs and the "map" is known as the coordinate plane. Grasping the concept of ordered pairs is essential in math because it's the foundation of graphing and understanding relations between numbers in a visual way.

## Understanding Ordered Pairs – Definition

An ordered pair is a pair of numbers used to locate a point on a coordinate plane. The first number is called the x-coordinate, and the second number is the y-coordinate.

Ordered pairs follow a specific format: (x, y). This format tells us the exact position of a point relative to the origin, where the x-axis and y-axis intersect.

### Rules for Ordered Pairs:

1. The first coordinate, x, indicates horizontal movement from the origin.
2. The second coordinate, y, indicates vertical movement from the origin.
3. Negative x values mean movement to the left, and negative y values mean movement down.

## Plotting Ordered Pairs – Example

Let's plot the point (3, -2) on the coordinate plane. Remember, the first number is the x-coordinate, and the second number is the y-coordinate.

1. Start at the origin (0,0).
2. Move 3 units to the right, as the x-coordinate is positive.
3. Move 2 units down since the y-coordinate is negative.
4. Place your point. You've now successfully plotted the point (3, -2).

## Graphing Equations Using Ordered Pairs – Guided Practice

Consider the equation y = 2x + 1. To graph this equation, we need to find ordered pairs that satisfy it.

What is an ordered pair that satisfies the equation y = 2x + 1 when x = 0?
What about when x = 2?
Now, plot these points and draw the line that passes through them.

## Understanding Quadrants and Axes – Explanation

The coordinate plane is divided into four sections known as quadrants. These quadrants are labeled with Roman numerals:

Quadrant I Top right, where both x and y are positive.
Quadrant II Top left, where x is negative, and y is positive.
Quadrant III Bottom left, where both x and y are negative.
Quadrant IV Bottom right, where x is positive, and y is negative.

The axes themselves—x-axis and y-axis—are also important. They divide the plane into quadrants and are used as reference lines to determine the coordinates of points.

## Slope Calculation – Summary

Key Learnings from this Text:

• An ordered pair tells us the position of a point on the coordinate plane.
• The x-coordinate is the first number, indicating horizontal movement.
• The y-coordinate is the second number, indicating vertical movement.
• The quadrants help us determine the sign of the coordinates.
• Distance and midpoint formulas are useful for finding the length and center between two points.
• The slope measures the steepness of a line on the graph.

If you're curious to delve deeper into the world of coordinates and want to master graphing, check out our interactive practice problems and engaging video content!

## Ordered Pairs – Frequently Asked Questions

What are ordered pairs used for in mathematics?
How do you determine which quadrant a point is in?
What is the significance of the origin in ordered pairs?
How can ordered pairs help in solving equations?
Is it possible for an ordered pair to have zero as one of its coordinates?
What does it mean if a point has the same x-coordinate but different y-coordinates?
Can two different points have the same ordered pair?
How do you plot an ordered pair when both coordinates are negative?
Why is it important to follow the order in ordered pairs?
Can ordered pairs be used in three-dimensional graphing?

## Ordered Pairs on the Coordinate Plane exercise

Would you like to apply the knowledge you’ve learned? You can review and practice it with the tasks for the video Ordered Pairs on the Coordinate Plane.

Hints

The coordinate point is written as the $x$ coordinate first and the $y$ coordinate second. $(x, y)$

The axes are set out like a number line with positive and negative numbers.

$(x, y)$

• $x$ is the horizontal axis
• $y$ is the vertical axis

We can see these example points are written:

• A $= (3, 2)$
• B $= (-2, 5)$
• C $= (-2, -2)$
• D $= (3, -5)$
Solution
• In Quadrant $1$ the $x$ and $y$ axis are positive numbers, so the coordinates are $(+, +)$.
• In Quadrant $2$ the $x$ axis is negative and $y$ is positive, so the coordinates are $(-, +)$.
• In Quadrant $3$ the $x$ and $y$ axis are negative numbers, so the coordinates are $(-, -)$.
• In Quadrant $4$ he $x$ axis is positive and $y$ is negative, so the coordinates are $(+, -)$.

Hints

The quadrants are laid out like this:

When a coordinate point has a negative $x$ and a negative $y$ we are moving left and down.

Point $(-4, -3)$ has both negatives $(-, -)$. This means we move left for $4$ and down for $3$.

Solution

$(-4, -3)$ is in quadrant $3$ because both the coordinates are negative numbers $(-, -)$.

We move left for $4$ and down for $3$, see diagram.

• ### Find the coordinate point.

Hints

To find each point:

• first move horizontally for the $x$ coordinate.
• second move vertically for the $y$ coordinate.

Here is how we found coordinate A.

• First we moved horizontally $3$ to get the $x$ coordinate.
• Second we moved vertically $5$ to get the $y$ coordinate.
• We would write this $(3, 5)$.

Solution
• A $= (3, 5)$ $3$ right, $5$ up
• B $= (5, -3)$ $5$ right, $3$ down
• C $= (3, -5)$ $3$ right, $5$ down
• D $= (-3, -5)$ $3$ left, $5$ down
• E $= (-5, 3)$ $5$ left, $3$ up
• ### Find the mistake.

Hints

The coordinate point is written across first, then up or down next.

It looks like this $(x, y)$.

For example, $(4, -5)$ is $4$ moves to the right from the origin and $5$ moves down from the origin.

This point is $(-3,8)$ because the $3$ is to the left, so it’s $-3$ and the $8$ is up, so it is $+8$.

The correct point is $(-3,8)$.

Solution

The mistake was at $(7, -5)$, it was $7$ left and $5$ down which is $(-7, -5)$.

The correct ones are:

• $(3, 2)$, $3$ right and $2$ up
• $(4, -2)$, $4$ right and $2$ down
• $(-2, -2)$, $2$ left and $2$ down
• $(-3, 8)$, $3$ left and $8$ up

• ### Find the coordinate.

Hints

We write coordinates by counting the $x$ or first number across/horizontally, then the $y$ or second number up or down/vertically.

$(x, y)$

The $x$ coordinate is $4$ to the right and the $y$ is $2$ down.

As a check we know it is in Quadrant $4$, so the coordinates should be in the order $(+, -)$.

Solution
• $(4, -2)$
• For the $x$ coordinate (the first number), we move $4$ across/horizontally.
• For the $y$ coordinate (the second number), we move $2$ down/vertically.
• As a check we know it is in quadrant $4$ which has $(+, -)$ coordinates.
• ### Form a square using the points.

Hints

A square has $4$ vertices of $90^\circ$ and $4$ sides of equal length.

We can see in this example that the red cross forms the square with the other points making the sides the same length and each vertex $90^\circ$, a right angle.

Solution

The correct answer is $(2, 7)$.