Where should Sam and Marla Wilson look for a new apartment that is equidistant from their jobs? anywhere on B street 1
12.6 Locus: A Set of Points In the warm up, you described the possible locations based on a certain condition. A locus is a set of points, all of which meet a stated condition. Loci is the plural of locus. 2
What is a sketch and description for each locus of points in a plane? The points 1 cm from a given point C C The locus is a circle with center C and radius 1 cm. 3
What is a sketch and description for each locus of points in a plane? The points 1 cm from AB A B The locus is a pair of parallel segments, each 1 cm from AB, and two semicircles with centers at A and B. 4
What is a sketch and description for each locus of points in a plane? The points 1 cm from AB A B The locus is a pair of parallel lines, each 1 cm from AB 5
You can use locus descriptions for geometric terms. The locus of points in the interior of an angle that are equidistant from the sides of the angle is an angle bisector. In a plane, the locus of points that are equidistant from a segment's endpoints is the perpendicular bisector of the segment. 6
Sometimes a locus is described by two conditions. You can draw the locus by first drawing the points that satisfy each condition. Then find their intersection. 7
What is a sketch of the locus of points in a plane that satisfy these conditions? The points equidistant from intersecting lines k and m The points 5 cm from the point where k and m intersect k m points A, B, C and D 8
What is a sketch of the locus of points in a plane that satisfy these conditions? The points equidistant from two points X and Y The points 2 cm from the midpoint of XY X Y points A and B 9
What is the locus of points in space that are c units from a point D? D The locus is a sphere with center at point D and radius c. 10
What is the locus of points in space that are 3 cm from a line l? l The locus is an endless cylinder with radius 3 cm and centerline l. 11
What is the locus in a plane of the points that are equidistant from two parallel lines? The locus is the line to and equidistance from the given lines midway between them. 12
What is the locus in a space of the points that are equidistant from two parallel planes? The locus is a plane to and equidistance from the given planes midway between them. 13
What is a sketch and description for each locus of points in a plane? Points 4 cm from a point X X The locus is a circle with center c and radius 4 cm. 14
What is a sketch and description for each locus of points in a plane? Points 2 in. from UV U V The locus is a pair of segments, each segment 2 in. from UV, and two semicircles with radius 2 in. and centers U and V. 15
What is a sketch and description for each locus of points in a plane? Points 3 mm from LM L M The locus is a pair of lines, each 3 mm from LM. 16
What is a sketch and description for each locus of points in a plane? Points 1 in. from a circle with radius 3 in. The locus is a two circles concentric with the original circle; the smaller circle has radius 2 in. and the larger circle has radius 4 in. 17
What is a sketch and description for each locus of points in a plane? Points 1 cm from the endpoints of CD C D The loci are circles with a radius of 1 cm centered at C and D. 18
What is a sketch and description for each locus of points in a plane? Points 2 cm from a given point P P The locus is a circle with center P and radius 2 cm. 19
What is a sketch of the locus of points in a plane that satisfy these conditions? The points equidistant from the endpoints of segment MN The points less than or equal to 2 cm from the midpoint of segment MN M N The locus is a segment of the perpendicular bisector of MN with a length of 2 cm on each side of MN. 20
Describe the locus (or loci) of points in space that are 5 cm from plane P. P two parallel planes in space that are 5 cm from the original plane 21
Describe the locus of points in space that are 3 in. from point Q. Q a sphere in space with a radius of 3 in. and center Q. 22