LOCI A locus is a set of points

LOCI

A locus is a set of points that satisfy a rule. It can be a line, a curve or a region.

1 Find the locus of points that are 5 cm from the point A. A The locus is a circle centre A, radius 5 cm.

2 Find the locus of points that are 3 cm from the line AB. A B The locus is made from two straight lines and two semicircles.

3 Find the locus of points that are the same distance from the line AB as they are from the line AC. B C A The locus is the bisector of the angle BAC.

4 Find the locus of points that are the same distance from the point A as they are from the point B. B A The locus is the perpendicular bisector of the line AB.

5 Find the locus of points that are equidistant from two given intersecting straight lines. D A B C The locus is made from two straight lines that bisect the angles.

6 The wheel is rolled along the ground. Draw the locus of the point P. Locus of P P

7 The equilateral triangle is rolled along the ground. Draw the locus of the point P. Locus of P P

8 Two goats are tethered by a piece of rope to opposite corners of a field. The pieces of rope are 9 meters long. The field is 10 metres by 14 meters. Find the locus of points that can be reached by both goats. Locus of points

9 Construct the locus of points that are 3 cm from triangle ABC. C A B

10 Construct the locus of points inside the triangle that are • nearer to the line AB than to the line AC • less than 4 cm from the point B Label the locus of points R. C First construct the bisector of angle CAB. Next draw the arc of a circle radius 4 cm with B as centre. R A B

11 Construct the locus of points inside the triangle that are • nearer to A than to B • nearer to the line AD than to the line AB Label the locus of points R. D C R First construct the perpendicular bisector of AB. Next construct the bisector of angle DAB. A B