Lesson Video: The Coordinate Plane: First Quadrant Mathematics • 5th Grade

Video Transcript

The coordinate Plane: First Quadrant

In this video, we will learn how to find the 𝑥- and 𝑦-coordinates of a point in the first quadrant and locate a point given its coordinates.

The coordinate plane is formed by a horizontal number line called the 𝑥-axis and a vertical number line called the 𝑦-axis. Each axis crosses each other at zero. The axis or the coordinate plane is divided into four sectors, which are called quadrants. This sector is called the first quadrant.

An ordered pair describes the location of a point on the coordinate plane. The first number is called the 𝑥-coordinate, and the second number is called the 𝑦-coordinate. So, the coordinates for the pink point marked on our coordinate plane are three, three. Let’s take a closer look at some coordinates.

Here we go. Our coordinate plane is made up of a horizontal number line called the 𝑥-axis and a vertical number line called the 𝑦-axis. And we know that each axis crosses each other at zero. And we know that an ordered pair describes the location of a point on the coordinate plane. We always write the 𝑥-coordinate first, followed by the 𝑦.

Did you notice all the points that have appeared on our coordinate plane? These points can be joined to make a picture. I wonder if you can work out what it is? We’ve joined some of the points. Can you tell what it is yet? I bet you can tell what it is now. Now that we’ve ready to tell you must have spotted that this is a dog. Let’s use some coordinates to give our dog an eye and a nose. This is where we’re going to draw our nose using a black circle.

The 𝑥-coordinate is always the first number in our ordered pair. If we draw a line from our point down to the 𝑥-axis, we can see the coordinate is one. And if we do the same with the 𝑦-axis, join our point along to the axis, we can see that the 𝑦-coordinate is seven. So, let’s draw on our nose at one, seven. There we go.

Now, we’ve got an eye. What are the coordinates for our dog’s eye? Let’s start by drawing a line from our point down to the 𝑥-axis. Here we go, which is number three. So, we know our 𝑥-coordinate is three. Now, we need to draw a line from our point to the 𝑦-axis. It reaches number seven. So, the coordinates, or the ordered pair, for our dog’s eye are three, seven. Let’s practice using coordinates now by answering some questions.

What is the 𝑥-coordinate of point 𝐴?

In this question, we have to write one of the coordinates for point 𝐴. We write coordinates as an ordered pair. We usually write the 𝑥-coordinate first. This number line is called the 𝑥-axis. This is the coordinate which we have to find. So, let’s draw a line from our point, point 𝐴, all the way down to the 𝑥-axis. Here we go, starting at 𝐴 all the way down to the 𝑥-axis. Our arrow is pointing to number three. So, the 𝑥 coordinate of point 𝐴 is three.

Write the ordered pair for the location of the monkeys.

In this question, we have to locate the monkeys on the coordinate plane. Here they are. We’ve marked them with the pink dot. Now, we have to write the ordered pair. An ordered pair describes the location of a point on the coordinate plane. The first number is called the 𝑥-coordinate, and the second number is called the 𝑦-coordinate. So, let’s start by locating the 𝑥-coordinate. To do this, we can draw a line from our point down to the 𝑥-axis.

Now, we can see the 𝑥-coordinate is four, and we can do the same to find the 𝑦-coordinate. We start at our point and draw a line across to the 𝑦-axis. Now, we can see our 𝑦-coordinate is five. And we need to place our ordered pair inside brackets. The ordered pair for the location of the monkeys is four, five.

Which point is at four, six?

In this question, we are shown five different points on our coordinate plane: points 𝐴, 𝐵, 𝐶, 𝐷, and 𝐸. And we have to identify the point which is at four, six. When we see an ordered pair or a pair of coordinates, we have to remember that the 𝑥-coordinate always comes first followed by the 𝑦-coordinate. So, we know that number four is the 𝑥-coordinate. If we start at four on the 𝑥-axis and draw a line going up, this will help us to identify which point is at number four on the 𝑥-axis.

So, let’s start drawing from four on the 𝑥-axis. Can you see which point we’re going to reach? It looks like our point is point 𝐸. But we need to check the 𝑦-coordinate, which is six. So, let’s find six on the 𝑦-axis and draw our line across until we reach a point. Here we go. Here’s six on the 𝑦-axis. And if we join our point along this line, again we reach point 𝐸. The point which is at four, six is point 𝐸.

What are the coordinates of the missing point which would complete the square?

In this question, we have to complete the partially drawn square, and then we have to write the coordinates of this missing point. Let’s start by thinking about where to draw the missing point. It would go here, let’s join up the points to complete the square. There we go. Now, we need to write the coordinates of this point. When we write a pair of coordinates, we always write the 𝑥-coordinate first.

This orange line is the 𝑥-axis. We need to draw a line from our point down to the 𝑥-axis. Now, we can see the 𝑥-coordinate is six. Let’s do the same to find the 𝑦-coordinate: draw a line from our point all the way along to the 𝑦-axis. The pink line shows our 𝑦-axis. And by drawing a line from our point to the 𝑦-axis, we can see the 𝑦-coordinate is three. The coordinates of the missing point which would complete the square are six, three. Our 𝑥-coordinate is six and our 𝑦-coordinate is three.

What have we learned in this video? We’ve learned how to find the 𝑥- and 𝑦-coordinates of a point in the first quadrant. And we also learned how to locate a point given its coordinates.