Points less than 2 cm from A and nearer to A than to B, AB = 3 cm

Step by step

The question

Question: shade the points that are less than 2 cm from A and nearer to A than to B, with A B = 3 cm.

Less than, and nearer: the edges themselves are not included.

So we draw them dashed.

1 Read the rules

A and B are 3 cm apart.

Two rules: near A, and nearer to A than to B.

2 Less than 2 cm from A

Points 2 cm from A make a circle.

Less than 2 cm: inside it.

Dashed, because the circle itself is not included.

3 Nearer to A than to B

Points the same distance from A and B are on the perpendicular bisector of A B.

Nearer to A: on A's side of it.

Careful!

The region must follow both rules.

Only the part that is inside the circle and on A's side.

4 Shade the region

Shade the part inside the circle, on A's side of the line.

5 Check

Let's check one point in the shaded part: it is 1 cm from A, less than 2 cm, and 4 cm from B, so nearer to A.

So it is right!

Let's look back.

First: read the rules.

Then: less than 2 cm from A.

Then: nearer to A than to B.

Then: shade the region.

Last: check.