Loci

What is a locus?

• A

locus

is

all the possible positions

can be describer by a rule that • E.g.

• Describe the locus of an object that is always

2cm from point D 2cm D

Try these:

• Draw a sketch of a locus that is always 8cm from line AB

B A

•Sketch the locus of an object that is always 4cm from point R

A

Answers

B 4cm R

Example

• Katy’s house is

3km from school

and 4km from the motorway.

• Find the

two possible positions

of Katy’s house.

4km Motorway School 3km

Questions

• A horse is

tied to a wall

. The length of the

rope is 4m

. Sketch the loci that the horse can reach.

• A

bull is tethered to a ring

in a farmyard. The

rope is 5m long

. Sketch the loci that the bull can reach.

Answers

Wall 4m 5m

Loci of Moving Objects

• If you made a

mark on a coin

and rolled it along a line it would make a pattern The curve it the

locus

of a point as the

coin moves forward

Bisecting An Angle

• Bisecting an angle means

splitting it exactly in half.

• You do this with a

compass Open you compass a fixed distance A You must keep it this distance 60 ° Make a curve by placing the point at A B Make another curve by placing the point at B Where the curves meet you can draw a line to split your angle in half

Bisecting A Line

• Two lines at

right angles

are

perpendicular

to each other

C A B D

•

You can draw the bisecting line

•

Measure Line AB and mark it at the halfway point

•

Draw two curves with a compass

Equidistant from two points

• All the points on the bisector line are

equidistant

the

two points at the ends of the original line

• E.g.

from • Points A and B are 7cm apart • Draw the locus of the points that are equidistant from AB

A 7cm B

Constructing A Perpendicular From A Point To A Line

• You want to draw a perpendicular line from point P to the line AB

A C P B D Draw a curve from point B that goes through AB Draw curves from C and D that cross below the Line Where the cross we will call that Q Q