Fill in the gap: We use a coordinate .............. to describe a location in 2-D space.

Fill in the gap: The ............. describes the horizontal location of a given point.

Fill in the gap: The ............. describes vertical location of a given point.

The origin is the point

What is the coordinate of point A in the image given below?

What is the coordinate of point B in the image given below?

What is the coordinate of point C in the image given below?

The 2-D coordinate axis

﻿Hello, and welcome to today's lesson with me, Dr. Saada. In today's lesson, we will be looking at line segments. For this lesson, you need a pen and a paper, so please make sure that you have these. And when you're ready, let's make a start. To start today's lesson, I would like you to try this. Put the line segments in order from the shortest to the longest. Explain how you compared their lengths. If you're feeling confident about this, please pause the video and have a go. If not, support is coming in three, two, and one. Let's look at line E. So if we look at line segment E, it goes across 2, so it has a length of 2 units. Let's look at D and compare it. D, it goes up 2 and 1 across. You can see that it takes a lot longer to get from one end of the line segment to the other end. Try and think about that robot question that we did in lesson one. Therefore, now I can say that D is longer than E because E is 2 to the right, but D is 2 up and 1 to the right. Now, pause the video and have a go at the rest of the question. And now, let's mark and correct the try now. Okay? So if we look at line C, we can see that it is 3 to the right. If we look at line B, line segment B, we can see that we need to go 1 up and 3 to the right. So it's a little longer than C. If we look at A, we have to go up 4 places, so up 4. If we look at line F, we need to go down 1 and 4 to the right, or 4 to the right and 1 down, it really doesn't matter. And for the last one, for G, we go up and then across, we go 4 up and 2 to the left, okay? And this is how they are in order. Please mark and correct your work. Well done if you had them correct. Now, I just want you to understand here something that it really doesn't matter, when I'm looking at the length of these lines, if I'm going up or down first, or if I'm going left or right. Because when I went to compare them, some of these lines could be... Because when I went to compare them, some of these lines would have been rotated. Today, were looking at line segments. So what is a line segment? A line segment is the portion of a line that connects two points. A line in mathematics goes forever in both directions whereas a line segment actually has an end, okay? Let's look at this grid here. I have three lines, line AB, line CD and line EF. Find the coordinates of the end points of each line segment below. What is the same and what is different about each line segment? So let's start by looking at the coordinates. This is something that we've covered in lesson one. Look at the grid for me. Look at point A. What is the coordinate of point A? Think about it. You've got it? Excellent. It is 0, 0. It's at the very important point, and that is called the origin, really good. Now, what is the coordinate of point B? Think about it. You've got it. Excellent. The coordinate is 4, 5. Remember, we always look at the x-coordinate first followed by the y-coordinate. And the x-coordinate for B is 4, and the y-coordinate is 5. Okay. What's the coordinate of point C? Good job. It's 3, -4. So it's 3 on the x-axis, -4 on the y-axis. What about point D? Good job. That is 7,1. What about point E? Think about it. You've got it. It is -6, -6. And what is coordinate of the last point? Correct. Well done. It's -4, -3. Now, what is the same and what is different about each line segment that we have here? Have a little think. Can you notice anything? Does it start maybe with different? Really good job. AB and CD are longer than EF. The line segment EF is the shortest out of the three lines. What is the same? Really good. AB and CD are the same length. If you look at line segment CD, if I want to get from point C to D, I need to go across 4 to the right, 4, and then up 5. It's exactly the same with AB. So to get from point A to point B, I need to go 4 to the right and 5 up, which tells me that the two line segments here are of equal length. And this brings us to the independent task. I would like you to pause the video, read the questions carefully and have a go at them. When you're done, press play again, and then we will mark and correct the work together. Off you go. Okay. Now, let's mark and correct the work together. Question number one. Identify the triangles where the highlighted line segment is the same length. So I'm giving you some line segments and you have, what looks like a triangle that has been highlighted for you just to help you with counting across and, and then above, or if you're going down from one end point to the other. Let's make a start. With line segment A, I need to go 1 across and 3 up. Line segment B, I need to go 2 to the right and 3 up. For C, I need to go 3 to the right and 3 up. None of them are equal so far, right? Let's look at D. And remember, it doesn't really matter which end you start with, they should give you the same thing. Okay. Let's look at D. I went to the right 3 and then down 1. Can you see any similarity here? With any of the other line segments? Which one does D match with? Good job. Let's look at the next one, F. Down 2 and to the right 3. And with E, excellent, to the right 3 and down 3. Now, which one's, which line segments are of equal length? They have the same length. Well, A and D are the same. One of them, you go 1 to the right and then up 3, and then other one, you go 3 to the right and then down 1. So you're covering the same journey. Think back about that robot question that we did in lesson one. Imagine that robot is actually walking this journey. It's covering the same distance in both A and D. Now, which other two line segments are of equal length? Good job. It's B and F. And next one, C and E. It's 3 to the right and 3 up, or 3 right and 3 down, so it's the same distance. Really good job. Well done. And question number two. Decide which of the line segments connecting each pair of coordinate is the longest. So let's look at the first pair. We have 4, 0, to 7, 0. So that's some line segment connecting from 4, 0, to 7, 0. Which tells me that this line segment is just going to the right 3 places. From 4 to 3, it's, 3 places. On the y-coordinate, it's not going up, it's not going down, they're both 0. Let's look at the next one, 8, 0 to 12, 0. It tells me that this line is moving from 8 to 12, so that's 4 to the right or to the left, depending on where you're starting from. But it's still going up or down because the y-coordinate is still 0. So which one is the longer? Excellent. The second one, B. What did you write down? Good job. So 9, 0 to 7, 0, we're going 2 to the left, or 2 to the right if you're starting from 7, 0 to 9, 0, depending on which way you're doing it. The next one. Excellent. 0, to 0 on the x-axis, we're not going anywhere, we're not going right to left. But 0 to 3 on the y-axis, we're going up 3 places. So the second line segment is the longer one. Next one, 4, 2, 9, 2. Okay. On the x-coordinate, we're going from 4 to 9, so we're going 5 places to that right. On the y-coordinate, we're not doing anything, we're not going up, we're not going down. So we are going 5 places to the right.

2, 4, -2, 8.

2 to -2, we're not going right, we're not going left, but we're going from 4 all the way to 8, we're going up 4 places. So out of these two, which is the longest one? Really. Good job. And next one, -2, 3 to -4, 3. So what are we doing? We're moving from -2 to -4, that is 2 places to the left. We're not going up or down because the y-coordinate is staying at 3. Next one, 7, 5 to 3, -5 So we're moving from 7 on the x-coordinate to 3 on the x-coordinate, that is a movement of 4 places to the left. And the y-coordinate will not, is not changing, it's -5, so we're not going up or down. Therefore, which one is the longer line segment out of these two? Excellent. It's this one. This brings us to the explore task. One of my favourite tasks of today's lesson. Tia used a triangle to find two points equidistant from the origin. Find more examples using this triangle. Okay. What equidistant sound like? Yeah, you're right. It sounds like equal distance, so it means equal distance from the origin. Where is the origin of the, of the grid? It's right here and it has the coordinate 0, 0. Well done. So Tia is trying to find two points that are exactly the same distance from that origin using this triangle here. So she took this triangle and she placed one here, and she place the other one here. By doing that, she created these two points here, this point and this point. Now, the two points are exactly the same distance from the origin. Now, from the origin to get to the top one, I need to go up 4 and then across 1. And to get to the next one, I need to go 4 across and 1 down. So all together, I'm still covering the same distance. Therefore, Tia can now say that -1, 4 and 4, -1 are equidistant from 0. So that coordinates of the two points that we labelled here. What I would like you to do now is pause the video and have a go at this question. Take that triangle and try place it at different places of the grid and see what you can come up with. I want points that are the same distance away from the 0. Pause the video and have a go. And here are some of my solutions where I took that triangle and I've placed it in different places to find points that were equidistant from the origin. You can see how I've placed my triangles here, and you can see the coordinates of the points that are all equidistant from the origin. If you've done this, you should be really, really, really proud of yourself that you've tackled a challenging question like this one. You have done a great job learning about line segments today. Please remember to complete the exit quiz to show what you know. Have a lovely day and enjoy the rest of your learning. I'll see you next lesson. Bye.

Which sentence correctly compares the lengths of the two line segments shown below?

Find the end points coordinates of the line segment shown below.

Which line segments has an equal length to (0, 0) to (3, 2).

Line Segments

In this lesson, we will learn to identify and compare line segments and use horizontal and vertical lengths of line segments.



Maths

Y7 Maths

Key Stage 3

Year 7

Line segments

Coordinates

Geometry

THEME

UNIT

Finding midpoints

Solving geometric problems

Forming shapes from midpoints

Forming shapes from diagonals

Equations of lines

Exploring horizontal and vertical lines

What are the co-ordinates of point C?

Which point has the co-ordinates (5, -2)?

Describe the movement from B to A.

Which statement best describes line segments A and B?

Which line segments have equal length?

Find the mid-­point of the points on the number line:

Fill in the gap: The equation .......... describes a line through every point with x-coordinate 4.

What is the equation for line C?

What is the coordinate of the midpoint of the line segment shown below?

Lesson overview:Line segments

Core Content

Coordinates: