AMSCO'S Geometry. New York - Rye High School

SolutionAnswerBCAB g CD g . The locus of pointsequidistant from two parallel lines isDCJFive Fundamental Loci 615Follow the procedure for finding a compound locus.(1) Since ABCD is a parallelogram,a third line parallel to the given linesand midway between them. In the EFfigure, EF gis equidistant from AB gand CD g.(2) The lines AB gand BC gare intersectinglines. The locus of points equidistantABfrom intersecting lines is a pair of linesGthat bisect the angles formed by thegiven lines. In the figure, GH gand JK gDgCJare equidistant from AB gand .E P Q F(3) The point P at which EF g intersects ABGH g and the point Q at which EF gK Hintersects JK gare equidistant from AB gand CD gand also equidistant from AB gand BC g.P and QNote that only point P is equidistant from the three segments that are sidesof the parallelogram, but both P and Q are equidistant from the lines of whichthese three sides are segments.ExercisesWriting About Mathematicsg1. If PQRS is a square, are the points that are equidistant from PQ gand RS also equidistantfrom P and S? Explain your answer.2. Show that the two lines that are equidistant from two intersecting lines are perpendicular toeach other.Developing SkillsIn 3–10, sketch and describe each required locus.3. The locus of points equidistant from two points that are 4 centimeters apart.