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Loci

Loci. 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. 2cm. D. Try these:. Draw a sketch of a locus that is always 8cm from line AB. B. A.

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Loci

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  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 2cm D

  3. 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

  4. Answers B A 4cm R

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

  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. Answers Wall 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 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 A 60° B Where the curves meet you can draw a line to split your angle in half

  10. Bisecting A Line • Two lines at right angles to each other are perpendicular 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

  11. 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 7cm B A

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

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