﻿Hello, and welcome to this lesson on introducing loci. My name is Mr. Maseko. Before you start this lesson, make sure you've a pen or a pencil, a ruler and something to write on. You also need some loose sheets of paper. So make sure you get all those things before you start this lesson. Okay. Now that you have those things let's get on with today's lesson. First try this activity. So, you have to take a piece of paper and mark two points on that piece of paper. You can mark them anywhere as A and B. You're going to fold the paper so that those two points come together and then draw a line where there's the crease. And then what do you notice about the relationship between the fold line and the points A and B? And draw a line that joins A and B. And then what do you notice about the line segment joining A and B and the fold line? Now, try this for many different points and see what you come up with. Pause the video here and give this a go. Okay. Now that you've tried this let's see what you've come up with. Well, you should have a piece of paper that looks something like this, There're lots of different points and lots of different fold lines between those points. Now, if I just take two of my points and I'm going to draw the line that's between them and you have to use a ruler for this but I'm trying to do this quickly, so I can show you. So you see, I folded my piece of paper and joined my two points and there was a line in between those two points. And the points, so I'm going to label the points that I used as A and B. Now, what do you think? What do you notice about the relationship between points B and point A and the fold line in between them? Well, you should have noticed that the distance from point A to the fold line is the same as the distance from point B to the fold line. Those two distances are the same. Now, it tells us no matter where you measure distance, and you can try this with the ruler now from anywhere on point A, so to the line and from point B to the line the distances will be the same. But what you just have to make sure is that the angle you're travelling at is, so you going to the exact same point on the line. You see? We're going to the same on the line. So if you go from point A to a point on the fold line and then from point B to that same point, those distances will be the same. Hah, now that's interesting. Now, another thing that you could have noticed is that the line segment AB meet your fold line at a right angle. Now here's a simplified image of what we're doing in the "try it now task". So, what we had before, no, we've already said that when we have our fold line, the distance from point A to a point on the fold line is the same as the distance from point B to that same point on the fold line. Now, what exactly does a fold line represent then? So today we're looking at what we call locus. Now, the plural of locus is loci. What a locus is, a locus describes a path that a point can take. So if you're in many paths, that would be loci but if we're just talking about one path, that's a locus. So this line, that fold line represents a locus. Now, what exactly does that locus represent? For that locus? That a locus of points, that's the locus of points, so it's a line or a path, a locus points that are, now, I'm going to introduce a new word here, equidistant from points A and B. Now, that word equidistant, what do you think it means? Good, that word just means equal distance. So, that fold line represents a locus of points to a path that is the same distance between point A and point B. So if you go from point A to anywhere on that line and then from point B to that same point, that distance would be the same as that distance. We've seen this already in the "try it now task." Again, no matter where you go on that line those distances will be the same as long as you end up at the same point on the line. And you can use your ruler, so you can try this and measure all those lines and you will see that anywhere on that line, the distance from point B to a point in the line is the same as a distance from point A to that same point on the line. And the word you want to use is equidistant, is equal distance. You can see? You've got the equal part and the distance part. It's a compound word. Now here's an independent task for you to try. So for each diagram, I want you to draw the locus of points that is equidistant from the points on the diagram. Pause the video here and give this the go. Okay. Now that you've done this, what should you come up with? Well, you should have folded your piece of paper so that those two points met and you would have had a fold line in between them. And then if you measure the distance from the fold line to each of your points those distances should be the same. And the angle that your line segment meets your fold line should be 90 degrees. We see that those two lines could then meet at a 90 degree angle. Those two lines are perpendicular. Those two lines are perpendicular cause they meet at a 90 degree angle. Now you should have done this for all the diagrams on your work sheets. For this explore task you are trying to find different loci. And the loci have to satisfy certain rules. Like for example, in this sentence we're looking for a locus of points that is equidistant from two points and passes through C and K. So we're looking through a local of points that passes through C and K and is equidistant between two points. Now, if you take your sheet and you fold it and your fold line is on CK, you'll notice we folded so that your fold line go through CK. You see that the points A and E meet, I an M meet, F and H meet. You should also notice that B and D meet or J and L also meet. Now try and complete those other sentences. Pause the video here and give this a go. Okay. Now that you've tried this, let's see what you've come up with. Now, we're looking for locus of points that is equidistant from E and K. Well, we have to join the point E to the point K. If you join the point E to the point K, what you should notice is that your locus of points passes through C and M. So if you join point E to K, the locus of points passes through C and M. That's the points that are equidistant from E to the locus and then from K to locus. So that is C and M. Now your next one says the locus of points that is equidistant from B and something passes through G and something. Okay. Well, if we go from point B, if you fold this on to point J, so you just fold your sheet on the point there, you'll notice that that locus of points is equidistant between B and J passes through G and F or G and H. So that's one way you could have done it. You could have also folded B to L and then your locus of points would have passed through G and J or G and D. The locus of points going to B and J passes through G and H. Or B an L could have been what? G and D. Now the locus of points equidistant from doesn't pass through any of the marked points. This one was more to find an error that you should have done but you should have noticed that if you folded from, let's say A to F you'd have had a locus of points that is in between there and that doesn't pass through any of the points that are on my diagram. You could have also gone the other way, you could have gone A to B, but we'll just do between A and F doesn't pass through any of the points on the diagram. Okay. Now, I really hope that you've learned something about loci today and how to find points that are equidistant between two marked points. Now, if you want to share any of the loci that you drew ask your parent or carer to share your work on twitter tagging @Oaknational and #LearnwithOak. I will see you again next time. Bye for now.

A locus describes ___________________.

A line equidistant between two points is _____________________.

Two lines that meet at a 90 degree angle are ___________.

The plural of locus is _______________.

What shape is this statement describing: A locus of points that are equidistant from a central point.

Introducing loci

In this lesson, we will be exploring drawing loci that are equidistant between two points.

Maths

Y9 Maths

Key Stage 3

Year 9

Constructions, congruence, and loci

Geometry

THEME

UNIT

Perpendicular bisectors

Angle bisectors

Triangle centres

Plan problems

Congruence

Congruence and triangles (Part 1)

Congruence and triangles (Part 2)

Perpendicular lines meet at a____________.

Bisect means to _______________.

What is the midpoint between the coordinates (3,5) and (9,11)?

To draw an angle bisector for the angle ABC we first have to _____________________.

In order to find the locus of points that are equidistant between two points you have to draw ___________________.

Which of the following describes the circumcentre?

Lesson overview:Introducing loci

Core Content

Constructions, congruence, and loci: