Lesson video

Hi, I'm Mr Bond, and in this lesson, we're going to learn how to draw loci around a point.

First, we need to think about what the word loci means.

A locus is a set of points that follow a particular rule or pattern, and loci is simply the plural of locus.

So, for example, what about if I want to draw the locus of points 20 metres from point A? Well, we can see point A marked with a cross.

To mark a point that was 20 metres away, I would simply need to measure a distance of 20 metres and mark another point.

So this is one point that's 20 metres from A.

I could do this again and measure another 20 metres away from A in a different direction, and then mark this point.

I could do that a number of times and mark lots of points that are 20 metres from point A.

What shape does this start to form? Hopefully you can see that it would form a circle if I drew lots of points.

Here's a question for you to try.

Pause the video to complete the task and resume the video once you've finished.

Here are the answers.

It's diagram two that's correct.

You can investigate this for yourself by drawing a square around a point on some square paper and then measuring from the point that your square's around to the vertex of that square, and then measuring from the point to the closest point on the edge, and these will be different.

Here's a task that I'd like you to think about, is the statement true or false? A locus around a point is always a circle.

Pause the video to complete the task and resume the video when you've finished.

This is true, the locus of the set of points around a point is always going to be a circle.

In this example, we're going to think about accurately drawing the locus of points five centimetres from the point C.

So to do this accurately, of course we're going to need a ruler.

To start, we're going to need a set of compasses.

First, we'll need to open up our compass to five centimetres.

Then, placing the point of our compass at C, we need to draw a circle around C because we know that the locus of points around a point is always a circle.

Now I'd like you to have a go at doing exactly what I've done.

I'd like you to draw the locus of points that are five centimetres from point C.

Pause the video to complete your task and resume the video once you've finished.

Here are the answers.

You could check your locus of points by measuring from the centre, C, to the circumference of your circle at several points and just double checking that it's five centimetres all the way round.

Here's another example.

Leanne wants to buy a house within 30 miles of her office.

Draw the locus of points to define the region in which Leanne can buy a house.

Use the scale one centimetre is equal to 10 miles.

Let's think about that scale.

One centimetre is equal to 10 miles, and Leanne wants to buy a house that's within 30 miles of her office.

So how many centimetres is equal to 30 miles? Well, it's three lots of 10 miles, so it's going to be three lots of one centimetre.

So three centimetres is going to be equal to 30 miles.

So to draw the locus of points, again, we'll need to use a ruler, get our compasses, open them up to three centimetres, then placing the point on the office, we need to draw a circle with a radius of three centimetres around the office.

So Leanne can buy a house that's anywhere within this circle.

Now it's your turn.

Pause the video to complete your task and resume the video when you've finished.

Here are the answers.

In this question, we had to take into account the scale.

We were told to use the scale one centimetre is equal to five miles, this means that 20 miles will be four centimetres, so you needed to draw the locus of points four centimetres from factory A.

And here's today's final question, pause the video to complete your task and resume the video when you've finished.

Here are the answers.

In this question, you had to draw two loci, one with a radius of four centimetres and one with a radius of 4.

5 centimetres, and the path lies between these two loci.

That's all for this lesson, thanks for watching.