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geometry Q3.28-3.31

QuestionAnswer
group of only the points that answer a description locus
when a locus contains only the points which answer the question exclusiveness
when a locus contains all the points which answer the description when a locus contains all the points which answer the description
two very essential characteristics of the loci exclusiveness and inclusiveness
the location of all the points and only those points that satisfy given conditions locus
two steps to proving a simple locus 1. Prove that every point on the assumed locus satisfies the given conditions. 2. Prove that every point that satisfies the given condition is on this assumed locus.
Theorem 47: The locus of points equidistant from two given points is the perpendicular bisector of the line joining the two points
Theorem 48: The locus of points within an angle equidistant from the sides is the line that bisects the angle
Corollary 48-1: The locus of points equidistant from two given intersecting lines is the pair of lines bisecting the angles formed by the given lines
Theorem 49: The locus of points equidistant from two parallel lines is the line parallel to each of the given lines and midway between them
Theorem 50: The locus of points a given distance from a given line consists of two lines, one on either side of the given line, each parallel to the given line and the given distance from it
Theorem 51: The locus of points a given distance from a given point is the circle described with the given point as center and the given distance as radius
Theorem 52: The locus of the centers of all circles tangent to a given line at a given point is the perpendicular to the line at that point
only one what can be drawn to a line at a point in the line perpendicular
the distance of a point from a circle means the shortest distance from the point to the circle; a straight line through the center of the circle
Created by: tatianaprince
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