Chapter 8: Loci in 2 Dimensions

8.1 Locus

• Definition: A locus is a path formed by a set of points that satisfies certain conditions in a plane or three-dimensional space.
• Shapes of 2D Loci: Can appear as straight lines, arcs, and curves.

Examples of Loci

1. Revolving Fan:
   • Point C on a blade of a revolving fan forms a circular locus.
2. Swinging Pendulum:
   • Point C on a pendulum forms a curved locus.
3. Rotating Board:
   • Rectangular board PQRS rotated 360° around pole MN forms a right cylinder.
4. Rotating Semicircular Board:
   • Semicircular board PQR rotated 360° around pole MN forms a sphere.

8.2 Loci in Two Dimensions

• 5 General Cases:

1. Equidistant from a Fixed Point:

   • Forms a circle centered at the fixed point.
   • Example: Construct a circle with a radius of 3 cm centered at point O.

2. Equidistant from Two Fixed Points:

   • Forms the perpendicular bisector of the line connecting the two points.
   • Example: Use a compass to mark arcs from points M and N, draw the bisector.

3. Constant Distance from a Straight Line:

   • Forms parallel lines to the original line.
   • Example: Draw lines parallel to line AB at a distance of 3 units.

4. Equidistant from Two Parallel Lines:

   • Forms a line parallel and through the midpoints of the two lines.
   • Example: Draw a line equidistant from lines AB and DC.

5. Equidistant from Two Intersecting Lines:

   • Forms the angle bisector of the intersecting lines.
   • Example: Draw intersecting arcs from lines PQ and PN, and connect through P.

Determining Locus with Multiple Conditions

• Example Problem:
  1. Draw the locus of X constantly 7 units from point A.
  2. Draw the locus of Y equidistant from lines AB and CD.
  3. Mark points of intersection between locus of X and Y.

• Chapter 8 Concept Map: Visual representation provided for review.
• Closing Remarks: Encouragement to like, share, and comment with questions.