Lesson video

Hi, I'm Mr. Bond, and in this lesson we're going to learn how to draw the locus of points, equidistant from two points.

This is the fourth lesson on loci, but again, it's important to remind ourselves what a locus is.

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

We're thinking about the locus equidistant from two points in this lesson.

So what if I wanted to find the locus of points equidistant from A and B? Well, equidistant means the same distance, so I'm looking for a point that's the same distance from A and the same distance from B.

So let's say that the distance between A and B is 14 centimetres at their closest point.

So the red cross is equidistant from A and B, seven centimetres from A, and seven centimetres from B, but that's at their closest point.

I could also measure two points 7.

4 centimetres from A and 7.

4 centimetres from B.

This point is still equidistant from A and B, but it's not seven centimetres away, it's 7.

4 centimetres away.

I could measure a point that's 10.

7 centimetres away from both A and B, or 8.

3 centimetres.

What are these points starting to form? They're starting to form a straight line, so this is the locus of points equidistant from A and B.

Let's have a think about how we'd draw this locus.

Just like we have for some of the other loci questions, we would use a compass.

So we'd start by putting our compass point at A, and opening the compass so that it's more than halfway between A and B, then we'd draw an arc, then we'd move the compass, keeping it opened up to exactly the same distance, and put the point at B, and now we'd draw another arc that intersects twice with our first arc.

Now if we get a ruler, and draw a straight line through the two points of intersection, we've drawn our locus that's equidistant from A and B.

Here's a question for you to try, pause the video to complete your task and resume the video when you've finished.

Here's the answer, this is just like the example that I've just shown you.

So you should have a vertical line drawn using two arcs, where the line is drawn through the two intersections.

Here's another question for you to try, again, pause the video to complete your task and resume the video when you've finished.

Here's the answer, the purpose of this question was to make you realise that the locus of points equidistant from two other points isn't always vertical, in this case it's horizontal, and in fact, it could be at any angle.

Here's another question for you to try, make sure you read this question carefully, rather than just having to draw the locus, you also need to shade a region.

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

Here's the answer, once you've drawn the locus of points that are equidistant from A and B, you had to shade in the side of the locus that's closer to A.

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

Here's the answer, in this case, the boat could be anywhere along the line shown, you don't need to draw the little diagrams of boats.

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