Section 7 1 Locus of Points A locus

Section 7. 1 Locus of Points • A locus is the set of all points and only those points that satisfy a given condition (or set of conditions). – All points of the locus satisfy the given condition – All points satisfying the given condition are included in the locus. 9/25/2020 Section 6. 5 Nack 1

Examples • Example 1: Describe the locus of points in a plane that are at a fixed distance r, from a given point (P). – The locus is a circle with center P and radius r. Figure 7. 1 p. 324 • Example 2: Describe the locus of points in a plane that are equidistant from two fixed points (P and Q). – The locus is the perpendicular bisector of PQ. Fig. 7. 2 • Alternate definition of a circle. A circle is the locus of points in a plane that are at a fixed distance from a given point. Ex. 3, 4 p. 325 9/25/2020 Section 6. 5 Nack 2

Theorems • Theorem 7. 1. 1: The locus of points in a plane and equidistant from the sides of an angle is the angle bisector. – We must prove two things: • If a point is in the locus, then it satisfies the condition. • If a point satisfies the condition, then it is a point on the locus. • Two-Part Proof p. 326 • Theorem 7. 1. 2: The locus of points in a plane that are equidistant from the endpoints of a line segment is the perpendicular bisector of the line segment. • Two-Part Proof p. 326 -7 Ex. 5 p. 327 9/25/2020 Section 6. 5 Nack 3