# Coordinate Planes

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## Exploring Coordinate Planes and Ordered Pairs – Introduction

Welcome to an exciting journey through the world of maths! It's time to discover the magic of coordinate planes and ordered pairs. Think of them as secret codes that help us find hidden spots on a treasure map. But instead of digging for gold, we're hunting for points on a grid. Ready to become a maths explorer? Let's dive in!

## Ordered Pairs – Definition

An ordered pair consists of two numbers written in a specific order within brackets, like this: (x, y). The first number represents a position on the horizontal axis, known as the x-axis, and the second number represents a position on the vertical axis, called the y-axis. Together, these numbers pinpoint an exact location on a coordinate plane.

### Rules for Working with Ordered Pairs

When reading and plotting ordered pairs, always start with the x-axis and then move to the y-axis. Remember, the format is always (x, y).

## Understanding the Coordinate Plane – Explanation

Imagine a grid with two intersecting lines, one horizontal (x-axis) and one vertical (y-axis). This grid is known as a coordinate plane. The point where the x-axis and y-axis cross is called the origin, and its ordered pair is (0, 0). Every other point on the plane is identified by its unique ordered pair.

## Plotting Points on the Coordinate Plane

To plot a point, like (3, -2), start at the origin. Then move along the x-axis 3 units to the right, since the x-value is positive, and move down 2 units on the y-axis because the y-value is negative. Mark the point where you end up and label (3, -2).

### Why Are Ordered Pairs and Coordinate Planes Important?

Ordered pairs and coordinate planes are vital tools in mathematics and many real-world applications, such as mapping, navigation and computer graphics. They help us visualise complex data and understand spatial relationships.

## Plots and Movements on the Coordinate Plane – Example

Using grid paper, draw an x and y axis, and let's plot some points together!

Find the point (3, 4) on the coordinate plane.

• Start at the origin and move 3 units to the right along the x-axis.
• Next move 4 units up since the y value is positive.

Find the point (-1, 2).

• Start at the origin move 1 unit to the left on the x-axis (since it's negative)
• Next move up 2 units up on the y-axis since the value is positive two.

Your graph should now have two points marked. Great job!

## Coordinate Plane – Guided Practice

Ready for more? Let's try plotting a few more points together.

Plot the point (-3, -5) on the coordinate plane. Where do you start and in which direction do you move first?

## Applying Ordered Pairs and Coordinate Planes

Now that we've practised plotting points, let's apply our knowledge.

## Summary of Coordinate Planes and Ordered Pairs

Key Learnings from this Text:

• Ordered pairs (x, y) tell us the exact location of a point on a coordinate plane.
• The first number in an ordered pair corresponds to the horizontal x-axis, and the second to the vertical y-axis.
• The origin (0, 0) is the starting point for plotting all points on the coordinate plane.
• Plotting points and connecting them can help us create shapes and solve geometry problems.

Keep practising with coordinate planes and ordered pairs, and explore other fun maths topics on our website. Check out interactive practice problems, videos and worksheets to help you become a maths champion!

## Coordinate Planes and Ordered Pairs – Frequently Asked Questions

What is an ordered pair?
How do you plot a point on the coordinate plane?
What is the origin on a coordinate plane?
Can ordered pairs have negative numbers?
What do you call the horizontal and vertical lines on a coordinate plane?
How do you find the distance between two points on a coordinate plane?
What shape do you get when you connect the points (0, 0), (0, 3), (3, 3), and (3, 0)?
Why is the ordered pair always written in the form (x, y)?
Can the same ordered pair point to two different locations on a coordinate plane?
What quadrant is the point (-3, 2) located in?

### TranscriptCoordinate Planes

Coordinate Planes. Cadet! Your mission, should you choose it, is to join the resistance, and seek and destroy incoming starships before they locate our fleet. You will need to locate the positions on a coordinate grid, or coordinate plane, and input their coordinate pairs into the missile launcher. We are depending on you! Good luck! Let's begin your training! A coordinate plane is formed when the horizontal, or , axis number line and the vertical, or , axis number line intersect at point zero, called the origin. This part of the coordinate plane is called a quadrant. We can determine the position of each point on the coordinate plane by identifying the coordinate pair corresponding to that exact location. We call the location of the pairs, the coordinates. Here is the location of one of our opponent's spaceships. To name the coordinates, first, identify the coordinate, which in this case is three. Then, identify the coordinate, which is five. We name this location three, five, and write the pair of coordinates like this. The order of the numbers is very important; you need to pay attention to the coordinate order to avoid ending up in the wrong location. Let's practise naming the coordinates of spaceship locations. What are the coordinates of this spacehip? Remember, look at the axis first, and then the . This coordinate is located at six, four. Which coordinates name the location of this point? The coordinates are seven, eight. For the final part of the mission, match all of the spaceships with their coordinates. Pause the video to solve, and resume when you are ready to review. The coordinate pair four, eight is found at . Three, one is located at . One, zero is at . Six, two is at , and zero, five is at Well done, cadet! By knowing the pairs of coordinates, you located their positions on the grid precisely.

## Coordinate Planes exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Coordinate Planes .
• ### Identify a co-ordinate of the vertex of a given shape.

Hints

What properties do you know about rectangles?

• They have 4 right angles.
• The opposite sides are parallel and equal to each other
• They are quadrilaterals and have 4 sides

When plotting a co-ordinate, the $x$ value comes first and then the $y$ value comes second. So a co-ordinate of $(4, 10)$ would be 4 across on the $x$ axis and then 10 up on the $y$ axis.

Coordinates are given as ordered pairs. The first number is the $x$ coordinate, which describes the horizontal position. The second number is the $y$ coordinate, which describes the vertical position.

Solution

The correct co-ordinate to complete the rectangle is $(8,7)$. As you can see on the axes now, by plotting this co-ordinate the rectangle has all the properties which make it correct!

• ### Identify the locations of different co-ordinates on a graph.

Hints

Remember, co-ordinates are plotted $x$ first and then $y$ second. This means you move vertically the $x$ amount first, and then horizontally the $y$ amount after. You might also know this as the saying "along the corridor and up the stairs!" as another easy way to remember how to plot co-ordinates.

A co-ordinate of $(4,3)$ would be plotted by moving 4 across horizontally to the right on the $x$-axis, and then 3 vertically upwards on the $y$-axis.

A co-ordinate of $(-5,-1)$ would be plotted by moving 5 across horizontally to the left on the $x$-axis, and then 1 vertically downwards on the $y$-axis.

Solution

The places you should have highlighted that the pirates needed to check for the treasures, are $(2,2)$ - the shipwreck, $(-7,7)$ - the jungle, $(-3,-7)$ - the kraken, $(7,8)$ - the skull cave and finally, $(2,-3)$ - the mermaid rock!

• ### Complete the passage of text.

Hints

Two lines that cross one another at 90-degrees are called perpendicular lines.

The $x$-axis is the horizontal axis and the $y$-axis is the vertical axis.

The point $(0,0)$ is called the origin.

Plotting co-ordinates can be helpful with graphing equations and mapping locations.

Solution

In mathematics, plotting coordinates helps us locate points on a grid. A co-ordinate grid has two perpendicular lines: the horizontal $x$-axis and the vertical y-axis. The intersection point of these axes is called the origin and is represented by (0,0).

To plot a point on the grid, we use co-ordinates. The first number shows the horizontal position on the $x$-axis, and the second number shows the vertical position on the $y$-axis. These numbers form an ordered pair, with the $x$-coordinate first, the $y$-coordinate second, separated by a comma, and enclosed in brackets.

To plot the point (3, 4), move three units right along the $x$-axis and four units up along the $y$-axis. The point (3, 4) is three units right and four units above the origin. Similarly, plot (-2, -5) by moving two units left and five units down from the origin.

By understanding how to plot coordinates, we can graph equations, map locations, and solve various mathematical problems accurately.

• ### Which co-ordinates have been plotted correctly?

Hints

Co-ordinates should be plotted using crosses and not dots! This is because crosses allow for greater accuracy.

Co-ordinates are plotted using the $x$ value first and then the $y$ value second.

Take care with the scale on the axes! Students often assume the scale always goes up in one's but it can be two's, five's, ten's or any amount.

All co-ordinates should be plotted by starting at the origin. As you get more confident with them you will get quicker at plotting them but this important fact is the basis of plotting all co-ordinates.

Coordinates are given as ordered pairs. The first number is the $x$ coordinate, which describes the horizontal position. The second number is the $y$ coordinate, which describes the vertical position.

Solution

This student has confused the order of the co-ordinate! They have forgotten that a co-ordinate gives information in the order $(x,y)$. The first value is the $x$ co-ordinate value and the second value is the $y$ co-ordinate value. The $x$-axis is the horizontal axis and the $y$-axis is the vertical axis.

• ### Finding Stars.

Hints

Find the key information in the question which is relevant to the problem.

Although the information about stars and constellation might be interesting, what key bits of information are relevant to actually answering the problem?

A co-ordinate presents two bits of information, an $x$ co-ordinate which represents how far you move horizontally on the $x$-axis, and the $y$ co-ordinate which represents how far you move vertically on the $y$-axis.

The $x$ co-ordinate value comes first in a co-ordinate pair, and then the $y$ co-ordinate value comes second.

For example, the co-ordinate $(3,2)$ gives an $x$ co-ordinate value of 3, and a $y$ co-ordinate value of 2.

Solution

The co-ordinate plotted at the point $(5,6)$ is highlighted on the illustration showing which star is the brightest in the constellation Ursa Major.

• ### Identifying a co-ordinate on a graph.

Hints

To find halfway between two numbers, you can add them together and then divide them by 2.

For example, to find the half way between 2 and 6, you can add them together (2 + 6) = 8, and then divide it by 2, which equals 4!

Find half way between the two $x$ co-ordinate values, and then find half way between the two $y$ co-ordinate values.

Halfway between the two points $(2,2)$ and $(6,4)$ is the point, $(4,3)$.

Solution

The new train station should be plotted at the point, $(6,7)$.