1. Loci

2. What is a locus? A locus is all the possible positions that can be describer by a rule E.g. Describe the locus of an object that is always 2cm from point D D 2cm

3. Try these: Draw a sketch of a locus that is always 8cm from line AB A B Sketch the locus of an object that is always 4cm from point R

4. Answers A B R 4cm

5. Example Katy’s house is 3km from school and 4km from the motorway. Find the two possible positions of Katy’s house. Motorway School 3km 4km

6. 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.

7. Wall Answers 4m 5m

8. 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

9. Bisecting An Angle Bisecting an angle means splitting it exactly in half. You do this with a compass 60° A B Open you compass a fixed distance You must keep it this distance Make a curve by placing the point at A Make another curve by placing the point at B Where the curves meet you can draw a line to split your angle in half

11. Bisecting A Line Two lines at right angles to each other are perpendicular BA C D You can draw the bisecting line Measure Line AB and mark it at the halfway point Draw two curves with a compass

12. Equidistant from two points All the points on the bisector line are equidistant from the two points at the ends of the original line E.g. Points A and B are 7cm apart Draw the locus of the points that are equidistant from AB A B 7cm

13. Constructing A Perpendicular From A Point To A Line You want to draw a perpendicular line from point P to the line AB A B P 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 C D Q