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You should already know:
- How to find the locus of a point equidistant from a fixed point.
- How to find the locus of a point equidistant from a line or line segment.
- How to combine simple loci.
You will learn:
- How to find the locus of a point equidistant from two fixed points.
- How to find the locus of a point equidistant from two lines.
- Combine simple loci.
Perpendicular Bisectors
We know that the locus of a point :
Bigger2. All the points that satisfy some conditions.
Here the condition is 3cm from A. In formal language we would say:
The locus of points equidistant from a fixed point is a circle.
The Top Three Loci
We have seen one of the most common loci - the circle. Here are two more you will come across:
If we have the condition 5cm from a line then we get another locus.
The locus of points equidistant from a fixed line is two lines parallel to the fixed line.
Now we will look at a more complicated example - the locus of points equidistant from a line segment.
Exam Tip
Don't rub out your construction lines - they show how you got the locus. It's OK to go over the final locus in colour or with a heavier pencil stroke so it stands out better but make sure the construction lines can be seen.
The locus of points equidistant from a line segment is a 'running-track' or 'capsule' shape.
So...
Let's try to solve a problem:
Quick Test
Q. Barry has tried to draw the locus of points equidistant from P and Q. What do you think he did wrong?
Q. Which of these shows the locus of points 3cm from the black L-shape?
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