Loci What is a locus A locus is

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Loci

Loci

What is a locus? • A locus is all the possible positions that can

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 2 cm from point D 2 cm D

Try these: • Draw a sketch of a locus that is always 8 cm

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

Answers B A 4 cm R

Answers B A 4 cm R

Example • Katy’s house is 3 km from school and 4 km from the

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

Questions • A horse is tied to a wall. The length of the rope

Questions • A horse is tied to a wall. The length of the rope is 4 m. Sketch the loci that the horse can reach. • A bull is tethered to a ring in a farmyard. The rope is 5 m long. Sketch the loci that the bull can reach.

Answers Wall 4 m 5 m

Answers Wall 4 m 5 m

Loci of Moving Objects • If you made a mark on a coin and

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. •

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 Make a curve by placing the point at A 60° 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 to each other are perpendicular

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

Equidistant from two points • All the points on the bisector line are equidistant

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

Constructing A Perpendicular From A Point To A Line • You want to draw

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 P B A D C Q Draw curves from C and D that cross below the Line Where the cross we will call that Q