Introduction

Coordinates provide a precise way to describe the location of a point. Instead of saying something is "near the top" or "a little to the left," coordinates tell us exactly where it is.

A coordinate plane is like a map with numbered horizontal and vertical lines. Every point on the plane has its own unique address, called an ordered pair.

Just as houses have street addresses, every point on a coordinate plane has a coordinate such as (4, 2) or (-3, 5).

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What is an Ordered Pair?

An ordered pair consists of two numbers written inside brackets.

Example:

(4, 2)

The numbers must always appear in this order:

• First number → x-coordinate
• Second number → y-coordinate

Think of it as:

(horizontal, vertical)

or

(across, then up/down)

The order is extremely important.

For example:

• (4, 2) is not the same point as
• (2, 4)

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Understanding the x-Coordinate

The x-coordinate tells you how far to move left or right from the origin.

• Positive x-values move right
• Negative x-values move left

Examples:

• x = 5 → move 5 units right
• x = –3 → move 3 units left

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Understanding the y-Coordinate

The y-coordinate tells you how far to move up or down.

• Positive y-values move up
• Negative y-values move down

Examples:

• y = 4 → move 4 units up
• y = –2 → move 2 units down

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How to Plot a Point

To plot any point:

Step 1

Start at the origin (0,0).

Step 2

Move left or right according to the x-coordinate.

Step 3

Move up or down according to the y-coordinate.

Step 4

Place a small dot.

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Example 1

Plot the point (3, 4)

1. Begin at (0,0)
2. Move 3 units right
3. Move 4 units up
4. Mark the point

Your point is now at (3,4).

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Example 2

Plot (-2,5)

1. Start at the origin.
2. Move 2 units left.
3. Move 5 units up.
4. Place the point.

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Example 3

Plot (4,-3)

1. Start at the origin.
2. Move 4 units right.
3. Move 3 units down.
4. Place the point.

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Naming a Point

Sometimes the point is already drawn.

Your job is to determine its coordinates.

To do this:

1. Look across to find the x-coordinate.
2. Look up or down to find the y-coordinate.
3. Write them as:

(x, y)

Always remember:

Across first, up or down second.

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Common Mistakes

❌ Writing the coordinates backwards

• (2,5) instead of (5,2)

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❌ Moving vertically before horizontally

Always move:

1. Horizontal (x)
2. Vertical

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❌ Forgetting negative signs

The point

(-3,2)

is completely different from

(3,2).

Negative numbers change the direction.

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Why Do We Use Coordinates?

Coordinates are used almost everywhere.

Examples include:

• GPS navigation
• Google Maps
• Video games
• Architecture
• Engineering
• Robotics
• Air traffic control
• Weather maps
• Computer graphics

Without coordinates, it would be difficult to describe exact locations.

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Worked Examples

Example 1

What point is shown?

The point is:

• 5 units right
• 2 units up

Answer: (5,2)

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Example 2

Plot (-4,-2)

Solution:

• Move 4 units left.
• Move 2 units down.
• Place the point.

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Example 3

Which coordinate is the x-coordinate?

Point:

(-7,3)

Answer:

x-coordinate = -7

y-coordinate = 3

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Did You Know?

Ships, aircraft, and satellites use systems of coordinates to determine their exact positions on Earth. GPS satellites can locate a position to within just a few metres—or even better under ideal conditions!

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Key Terms

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Key Takeaways

• Every point has a unique address called an ordered pair.
• Coordinates are always written as (x, y).
• Move across first, then up or down.
• The x-coordinate tells horizontal movement.
• The y-coordinate tells vertical movement.
• Coordinates help us describe locations accurately in mathematics and everyday life.