Lesson video

Hi, I'm Mr. Bond.

And in this lesson, we'll be drawing loci from line segments.

First, let's have a recap of what the word 'locus' means.

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

' So, now let's think about loci from a line.

For example, what about if I wanted to draw the locus of points, three centimetres from the line segment AB.

Well, let's start at A, and I'll measure three centimetres perpendicularly away from AB, like this.

I'll plot a point.

So this is a point that's three centimetres from the line segments AB.

Moving across from A to B, I could keep doing this, measuring points that are three centimetres away from the line segment AB.

I could do the same thing below the line segment AB.

But what about at either end? Well, effectively, I'm finding the locus of points from point A.

And if you remember, the locus of points away from a point follows a semicircular path.

So it would look like this.

And the same would happen at B.

So now let's think about connecting each of these points to see what it would look like as a whole locus of points.

First, connecting the points across the top, we'd have a line segment that's parallel to the line segment AB and the same length as the line segment AB.

And we'd also have the same thing beneath the AB.

Now looking at the points that are three centimetres away from B on the right-hand side, these form a semicircle, and the same thing happens at point A.

So this is the locus of points three centimetres from the line segment AB.

Now let's think about how we can actually draw this accurately without having to draw lots of separate points.

In this example, we want to draw the locus of points that are four centimetres away from the line segment CD.

First, let's think about what would happen at either end of the line segment.

We saw that in our last example, that the locus of points would be a semicircle.

So to help us draw this, we'll draw a circle at C.

It needs to be four centimetres in radius.

There it is.

We need to do exactly the same thing at point D.

Now, we need to draw the two line segments that are the same length as CD and parallel to CD.

We need to draw line segments that are tangent to the circles at C and D.

So we can see that drawing the circles first really helps us, but at the moment, this diagram doesn't show the locus of points that are four centimetres away from the line segment CD.

Because we only want semicircles at either end, not the full circles that are currently there.

So we need to rub out the lines that are inside the shape.

So there we have the locus of points that are four centimetres away from the line segment CD.

Now it's your turn.

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

Here are the answers.

Hopefully you've used my tip of drawing a circle at either end and then rubbing out the part of the circle that you don't need.

Here's another question for you to try.

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

Here are the answers.

This question was almost identical to the previous question but we needed to draw semicircles at either end with a radius of 4.

5 centimetres, and then connect these with a line segment tangential to the semicircles and parallel to the line segment XY.

Here's a third question for you to try.

Again, pause the video to complete your task and resume the video once you're finished.

Here are the answers.

Sana is correct.

Seb's will be more than two centimetres away if you measure from one of the points either C or D into the vertex of the rectangle.

And here is today's final question.

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

Here are the answers.

Once again, we needed to think about the scale that's involved.

We're told that one centimetre is equal to 0.

25 metres.

So if Simon wants to put a small fence exactly one metre around his flowers, one metre is four lots of 0.

25 metres.

So it would need to be four centimetres away on our diagram.

That's all for this lesson.

Thanks for watching.