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Points 3 cm from A

Step by step, with the reason for every step · Loci · Geometry

Step by step

The question

Question: draw the locus of the points that are 3 cm from a point A.

points 3 cm from A

A locus is the set of all the points that follow a rule.

Here: exactly 3 cm from A.

locus = all the points that follow the rule

1 Try some points

Some points 3 cm from A, in different directions.

They all lie on a circle.

2 Draw the locus

Open the compass to 3 cm and draw a full circle around A.

Every point on it is 3 cm from A.

Careful!

The locus is only the circle itself.

Points inside are less than 3 cm away.

Careful: exactly 3 cm = the circle line, not the inside

3 Check

Let's check: measure from A to any point of the circle: 3 cm.

So it is right!

any point on the circle: distance to A = 3 cm

Let's look back.

First: try some points.

Then: draw the locus.

Last: check.

Answer
points 3 cm from A

Your turn

Try this one yourself, then check:

points 5 cm from A
Show the answer
a circle, centre A, radius 5 cm

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