High School Math based on the topics required for the Regents Exam conducted by NYSED. The basic locus theorem and and compound loci.

Lesson on the laws of locus and compound loci.

This lesson is aligned with the NYS Regents Geometry Curriculum.

Related Topics: More Geometry Lessons

11) The distance between parallel lines l and m is 12 units. Point A is on line l. How many points are equidistant from linea l and m and 8 units from point A?

12) Mari's backyard has two trees that are 40 feet apart. She wants to place lampposts so that the posts are 30 ft from both of the trees. Draw a sketch to show where the lampposts could be placed in relation to the trees. How many locations for the lampposts are possible?

Loci 1

Loci 1 - describing and drawing the locus of all points following certain rules.

1) Locus of all points exactly 5 m from point P.

2) Locus of all points less than 5 m from point P.

3) The locus of all points that are within 3 m from the line AB.

4) The locus of all points inside the rectangle which are closer to A than to C.

5) The locus of all points inside the triangle that are closer to the line AB than to the line AC.

Loci 2

More on locus of points following rules, this time when more than one rule is being followed.

1) A lawn is to be planted inside a garden, at least 4 m from the side of the house and at laest 3 m fro the tree (T). Shade the lawn.

2) A rosebed is to be planted within 5 m of A and and within 6 m of C. Shade the rosebed.

3) Caroline wants to plant a lawn which is closer to side AB than AD, and within 6 m of C. Shade her lawn.

Locus Pocus

Iluustrates the following locus theorems:

**Locus Theorem 1**: The locus of points at a fixed distance, d, from point P is a circle with the given point P as its center and d as its radius.

**Locus Theorem 2**: The locus of 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.

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