Related Pages The following diagrams give the locus of a point that satisfy some conditions. Scroll down the page for more examples and solutions. When a point moves in a plane according to some given conditions the path along which it moves is called a locus. (Plural of locus is loci.). CONDITION 1: A point P moves such that it is always m units from the point Q. Locus formed: A circle with center Q and radius m. Example: Solution: CONDITION 2: A point P moves such that it is equidistant form two fixed points X and Y. Locus formed: A perpendicular bisector of the line XY. Example: Solution: CONDITION 3: A point P moves so that it is always m units from a straight line AB. Locus formed: A pair of parallel lines m units from AB. Example: Solution: CONDITION 4: A point P moves so that it is always equidistant from two intersecting lines AB and CD. Locus formed: Angle bisectors of angles between lines AB and CD. Example: Example: Five Fundamental Locus Theorems And How To Use Them Locus Theorem 1: The locus of points at a fixed distance, d, from the point, P is a circle with the given point P as its center and d as its radius. Locus Theorem 2: The locus of the points at a fixed distance, d, from a line, l, is a pair of parallel lines d distance from l and on either side of l. Locus Theorem 3: The locus of points equidistant from two points, P and Q, is the perpendicular bisector of the line segment determined by the two points. Locus Theorem 4: The locus of points equidistant from two parallel lines, l1 and l2, is a line parallel to both l1 and l2 and midway between them. Locus Theorem 5: The locus of points equidistant from two intersecting lines, l1 and l2, is a pair of bisectors that bisect the angles formed by l1 and l2. Example 1: Example 2: Example 3:
Five Rules Of Locus Theorem Using Real World Examples Locus is a set of points that satisfy a given condition. There are five fundamental locus rules. Rule 1: Given a point, the locus of points is a circle. Rule 2: Given two points, the locus of points is a straight line midway between the two points. Rule 3: Given a straight line, the locus of points is two parallel lines. Rule 4: Given two parallel lines, the locus of points is a line midway between the two parallel lines. Rule 5: Given two intersecting lines, the locus of points is a pair of lines that cut the intersecting lines in half.
Intersection Of Two LociSometimes you may be required to determine the locus of a point that satisfies two or more conditions. We could do this by constructing the locus for each of the conditions and then determine where the two loci intersect. Example: Solution: The points of intersections are indicated by points X and Y. It means that the locus consists of the two points X and Y. Example: Solution: Note: A common mistake is to identify only one point when there could be another point which could be found by extending the construction lines or arcs; as in the above examples. GCSE Maths Exam Questions - Loci, Locus And Intersecting Loci Examples:
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