A locus (pl. loci) is a Set of Points satisfying

certain criteria.

For A.S 1.4 Use Geometric Techniques to

Produce a Pattern or Object.Internal, 2 Credits

Section

Single LineSingle Point Two Fixed Points Two Fixed Lines

LOCI

Constructing the set of points Equidistant from a point A:eg. construct the set of points 3cm from Point A. (click once to start)

1. Construct the circle, centre A with radius 3cm.

3 cm

A

This is the set of

points equal to 3cm from point A.

Locus of points related to a Single Point

Equidist1 Within(1pt) Less than(1pt) Greater than(1pt)

Constructing the set of points within a certain distance from a point:eg. construct the set of points within 3cm from Point A. (click once to start)

1. First construct the set of points equal to 3cm from point A - ie the circle shown.

3 cm

2. Shade the area inside the circle

A

The shaded area is the set of points

less than or equal to 3cm from point A

Locus of points related to a Single Point

Equidist1 Within(1pt) Less than(1pt) Greater than(1pt)

Constructing the set of points less than a certain distance from a point:

Use a dashed line on the circumference to show that the circumference itself is not included.

3 cm

A

The shaded area is the set of points

less than 3cm from point A

Locus of points related to a Single Point

Equidist1 Within(1pt) Less than(1pt) Greater than(1pt)

Constructing the set of points greater than a certain distance from a point:

(Use a dashed line on the circumference to show that the circumference itself is not included.)

Shade outside the circle.

3 cm

Within(1pt)

A

The shaded area is the set of points

greater than 3cm from point A

Locus of points related to a Single Point

Less than(1pt)Equidist1 Greater than(1pt)

The Locus of Points equidistant from a fixed Line (click once to start)

Eg. The locus of points 3 cm from line AB.

B

A3 cm

There are two lines 3cm from line AB

Locus of points related to a Fixed Line

fixed Line fixed Line Segment

The Locus of Points equidistant from a fixed Line Segment(click once to start)

Eg. The locus of points 3 cm from line segment AB.

Locus of points related to a Fixed Line

B

A3 cm

There are two semicircles as well as two lines

fixed Line fixed Line Segment

The set of Points equidistant from two fixed points A and B(click once to start)

Bisect the line joining A and B

B

ALocus of points related to Two Fixed Points

Closer to pt A than BEquidistant to2 pts

The set of Points closer to point A than Point B(click once to start)

1. Bisect the line joining A and B

B

ALocus of points related to Two Fixed Points

2. Shade the side closer to A than B.

3. Make the line dashed to show that it is not included in this set of points.

Closer to pt A than BEquidistant to2 pts

Locus of Points Equidistant to two Fixed Lines. (click once to start)

B

A

C

D

1. Bisect angle AXC and extend

X

2. Bisect angle AXD and extend

Each point on the line is the same distance from AB as CD

Locus of points related to Two Fixed Lines

Closer to line AB than CDEquidistant to2 lines

Locus of Points Closer to Line AB than Line CD. (click once to start)

B

A

C

D

1. Bisect the angles

X

Locus of points related to Two Fixed Lines

2. Then shade the area on AB’s side of the angle bisectors

3. Make the lines dashed if they are not included in this set of points – consider the wording of the problem carefully

Closer to line AB than CDEquidistant to2 lines

Notes and Exercises

1. Copy Notes from Gamma pages

2. Do locus exercise together

3. Then finish of pages 69 and 70 your workbook.