The document discusses two-dimensional loci and their construction. It defines locus as the path of a moving point or set of points satisfying given conditions. Examples of loci include circles, lines, ellipses, and arcs. The key types of loci are those where a point is a constant distance from a fixed point or line, equidistant between two fixed points, and bisecting the angle between two intersecting lines. Intersection of two loci occurs at points satisfying the conditions of both loci.

1. 9 LOCI IN TWO DIMENSIONS Prepared by : Rosila Othman

2. Locus is the path of a moving point or a point or set of points that satisfies given conditions. 9.1 TWO DIMENSIONAL LOCI A figure of ‘8’ A circle

3. circle vertical line pentagon square triangle curve / arc

7. The locus of a moving point P that is at a constant distance from a fixed point O is a circle with centre O . Locus of P The locus of P is a circle with radius OP and centre O . O P

8. The locus of a moving point R equidistant from two fixed points A and B is the perpendicular bisector of the line AB . The locus of R is the perpendicular bisector of AB . || || A B Locus of R

9. The locus of a moving point that is a constant distance from a straight line AB are two straight lines that are parallel to AB . The locus are two lines ST and UV that are parallel to AB . A B U V = = Locus S T

10. The locus of a moving point that is at equidistant from two intersecting lines AB and CD is a pair of straight lines which bisect the angles between the two intersecting lines. The locus are two straight lines PQ and RS which bisect the angles between the two intersecting lines. A B C D P Q R S Locus

11. Determine the locus of the points which satisfy the given condition A circle with centre O and a radius 6 cm. Two straight lines parallel to AB and 3 cm from line AB. Two angle bisectors. The perpendicular bisector of the line EF. A point P moves such that it is equidistant from the point E and F. A point P moves such that it is equidistant from two intersecting line AB and CD. A point P moves such that it is 3 cm from the line AB. A point P moves at a distance of 6 cm from a fixed point O.

17. || || Locus of P Locus of Q Locus of W 1 cm 1 cm B C Locus of W A

18. Locus of Q 1.5 cm Locus of R

19. Locus of S Locus of T 1 cm 1 cm B C Locus of T

20. Locus of U

21. The intersection of two loci is the point or points that satisfy the conditions of the two loci. The points of intersection of two loci that is (a) equidistant from A and B , (b) a constant distance from A . The points X and Y are the points of intersection of the two loci. 9.2 INTERSECTION OF TWO LOCI X Y Equidistant from A and B . A constant distance from A . A × B ×

22. Locus of Y Locus of X  

23. Locus of X Locus of Y  

24. || || Locus of X  Locus of Y

25. Locus of Q Locus of P Two intersection  

26.  Locus of X || || Locus of Y  Two intersection

27. Locus of X  Locus of Z Locus of Y