LociObjectives:Grade DUnderstand the idea of a locusGrade CConstruct accurately loci, such as those of pointsequidistant from two fixed points

Solve loci problems, such as identifying pointsless than 3cm from a point P.Prior knowledge:Construct the perpendicular bisector of a lineConstruct the bisector of an angle

LociA Locus is the path followed by a moving pointLoci is the plural of locus1.The locus of points from a point P ....xP5 cm... is a circle radius 5 cm, centre PLoci can come in various forms:

Loci2.The locus of points the same distance from line ABThe locus of points 2 cm from line AB2 cm

Loci3.The locus of points equidistant from two fixed pointsA and Bequidistant means: same distance from locus of points equidistant from A and B(perpendicular bisector of AB)

Loci4.The locus of points equidistant from two fixed lines AB and AC locus of points equidistant from AB and AC(angle bisector of angle BAC)

LociImportant Note For a rectangular shape a locus inside is different from a locus outside InsideOutsideSharp cornersRounded corners

LociWorked Example 1A dog is on a 2 metre lead which is tethered to a 5m long pole in the centre of a garden. The garden has a flower border of m inside the garden wall. Show the loci of these on the diagram below.Flower borderScale: 1 large square = 1 metre

LociWorked Example 2A treasure chest is buried on an island. The map of the island is below.The treasure is equidistant from A and B and also equidistant fromC and D. Mark the position of the treasure on the map.ABDC locus of points equidistant from A and B locus of pointsequidistant from C and DX

LociQuestion 18 cm6 cm

LociQuestion 2Mark 2 points A and B, which are 10 cm apartConstruct the locus of all the points that are exactly 6 cm from BShade in all the points that are less than 6 cm from B and closerto A than B

LociQuestion 3A rectangular lawn is 12 m long and 10 m wide.The gardener has three sprinklers, which spray water in a circle of radius 3m.Sprinkler A is 3m from the top edge and 3m from the left edge.Sprinkler B is 3m from the top edge and 3m from the right edge.Sprinkler C is 3m from the bottom edge and 6m from the left edge.Make a scale drawing of the garden and shade the area that is covered by more than one of the sprinklersABC

LociQuestion 4The shape ABCD below represents a field on a scale of 1 cm to 10 m.Construct a line AE such that it bisects angle BAD and E is a point on the line BCConstruct the locus of points that are 40m from E Shade the area of the field that is more than 40 m from E and closer to AB than ADEConstruct the angle bisectorConstruct the locus around E4cm (40m)

LociWorked Example 1A dog is on a 2 metre lead which is tethered to a 5m long pole in the centre of a garden. The garden has a flower border of m inside the garden wall. Show the loci of these on the diagram below.Scale: 1 large square = 1 metre

LociWorked Example 2A treasure chest is buried on an island. The map of the island is below.The treasure is equidistant from A and B and also equidistant fromC and D. Mark the position of the treasure on the map.ABDC

LociQuestion 1

LociQuestion 2Mark 2 points A and B, which are 10 cm apartConstruct the locus of all the points that are exactly 6 cm from BShade in all the points that are less than 6 cm from B and closerto A than B

LociQuestion 3A rectangular lawn is 12 m long and 10 m wide.The gardener has three sprinklers, which spray water in a circle of radius 3m.Sprinkler A is 3m from the top edge and 3m from the left edge.Sprinkler B is 3m from the top edge and 3m from the right edge.Sprinkler C is 3m from the bottom edge and 6m from the left edge.Draw the garden and shade the area covered by the sprinklers

LociQuestion 4The shape ABCD below represents a field on a scale of 1 cm to 10 m.Construct a line AE such that it bisects angle BAD and E is a point on the line BCConstruct the locus of points that are 40m from E Shade the area of the field that is more than 40 m from E and closer to AB than AD