1. AIM : How do we find the locus of points ? Do Now: If all of your classmates were to stand 5 feet away from you, what geometric shape would your classmates be forming? The students would be forming a circle around you. In terms of the theorem, you are the center point, P, and the fixed distance is 5 feet. Homework : Regents sheet

2. How Do We Find Locus? 1. Draw a diagram showing the given lines and points. 2. Read carefully to determine the needed condition. 3. Locate one point that satisfies the needed condition and plot it on your diagram. Locate several additional points that satisfy the condition and plot them as well. Plot enough points so that a pattern (a shape) is starting to appear. 4. Through these plotted points draw a dotted line to indicate the locus (or path) of the points.

3. How Do We Find Locus? 5. Describe in words the geometric path that appears to be the locus. 6. If TWO conditions exist in your problem (a compound locus), repeat steps 2-4 above for the second condition ON THE SAME DIAGRAM. Count the number of points where the two loci intersect. (Where do the dotted lines cross?)

9. WORKSHEET ANSWERS 1. The locus of points will be two lines parallel to the given line y = -1 and at a distance of 2 units away from the line. The equations of the lines will be y = 1 and y = -3.

10. 2. The locus of points which describes the outer edge of the broadcasting range will be a circle with a radius of 24 miles. The radio station will be the center of the circle.

11. 3. The flowers will be planted 2 feet from the edge of the driveway and on either side of the driveway. If the driveway is 8 feet wide, the distance from the center to either edge is 4 feet. The 25 feet given in the problem is needed only to mention that the flowers will be planted the full 25 feet of the driveway (on both sides).

12. 4. The locus of points will be a straight line halfway between the two points. In this problem, the distance between the points is 6 units, so the line is drawn so that it is 3 units from each point. The equation of the line will be x = 1.

13. 5. The locus of points will be a straight line halfway between the given two lines and parallel to the lines. In this problem, the distance between the given lines is 5 units, so the locus line is drawn so that it is 2 and 1/2 units from each given line. The equation of the locus line will be y = 1/2.

14. 6. The locus will be a pair of angle bisectors which bisect each quadrant of the graph. The equations of these lines will be y = x and y = -x.

15. 7. The electrical cable should be placed perpendicular to a line segment connecting the two houses and crossing that line segment at a point 90 feet from each house. In this way, each point on the cable will be the same distance from each house.

16. 8. The answer will be 2 points. Notice where the two loci intersect marked with "X". The red line is first locus condition and the blue circle is the second locus condition.