Name: Date: ________________ Common Core Geometry - Honors Compound Locus AIM: What are compound locus problems and how do we solve them? Do Now: Write the equation of the lines that are equidistant from the x and y - axes. Homework: Worksheet Solving Compound Locus Problems: 1. Draw the “given.” 2. Draw the first locus on your “given” diagram. 3. Draw the second locus on your “given” diagram as well. 4. Determine how many times your two loci intersect (if the problem calls for graph paper, you may need to determine the coordinates of the intersections). 1.) The distance between points P and Q is eight units. How many points are equidistant from P and Q and also five units from Q? Show your work 2.) The distance between parallel lines L and M is 12 units. Point A is on line L. How many points are equidistant from L and M and also 8 units from point A? 3.) In the coordinate plane, what is the total number of points 5 units from the origin and 7 units from the y-axis? 4.) Two boulders are 20 feet apart. Bill wants to plant trees that are 12 feet from each boulder. In how many spots could he plant his trees? Draw a diagram. 5.) Show how many points are equidistant from 2 intersecting lines and also 3 inches from the point of intersection of those lines. Draw a diagram 6.) How many points are equidistant from points P(2,1) and Q(2,5) and also 3 units from the origin? Show your work! 7.) A spy infiltrates an enemy camp and captures a classified document which contains the coordinates to landmines that protect the camp. A tree is located thirty feet east of a fence that runs north and south. The landmines are buried 15 feet from the fence, and 20 feet from the tree. Your mission, find and disarm the landmines. 8.) In the accompanying diagram, point P lies 3 centimeters from line . How many points are both 2 centimeters from line and 1 centimeter from point P? 9.) What is the number of points in a plane two units from a given line and three units from a given point on the line? 10.) Two points A and B are 6 units apart. How many points are there that are equidistant from both A and B and also 5 units from A? 11.) A given point P is 10 units from a given line. How many points are 3 units from the line and 5 units from point P? 12.) a. Draw the locus of points equidistant from the points (4,1) and (4,5) and write the equation for this locus. b. Draw the locus of points equidistant from the points (3,2) and (-4,2) and write the equation for this locus. c. Find the number of points that satisfy both conditions stated in a and b. Give the coordinates of each point found. General Locus Problems: 1.) What is the equation of the locus of points 5 units away from the y - axis? 2.) a.) What is the equation of the locus of points equidistant from the lines y = -2 and y = 3? b.) What is the equation of the line that is equidistant from the lines 1 1 y x 3 and y x 1 2 2 3.) Describe the locus of points 2 units from the line y = -1. 4.) Find the equation for the locus of points equidistant from points A(3,5) and B (-7,5). 5.) Find the equation for the locus of points equidistant from points A(2,-9) and B (2,6). 6.) a.) Write the equations for the locus of point 3 units from the y – axis. b.) Write the equations for the locus of point 4 units from the line y = x. .