Loci and Regions

1. 1 A locus is the set of all points satisfying a given condition. 'Where can you stand if you must always be exactly 3m from this wall?' (A line parallel to the wall, 3m away.) 'From this post?' (A circle, radius 3m.) Introduce the term with physical examples.
2. 2 Display and construct each: (1) Fixed distance from a point → circle. (2) Fixed distance from a straight line → parallel lines (and semicircles at ends). (3) Equidistant from two points → perpendicular bisector. (4) Equidistant from two lines → angle bisector. Students sketch each.
3. 3 Using compass and ruler: construct the locus of points 3cm from point P (circle, radius 3cm). Construct the locus of points equidistant from points A and B (perpendicular bisector). Students construct both neatly on plain paper.
4. 4 A goat is tied to a post with a 4m rope. Shade the region it can reach. It is also at least 2m from a fence (draw the fence). Shade the region satisfying both conditions. 'The overlap of the two regions is where the goat can eat the grass.'
5. 5 Region within 3m of P: distance from P ≤ 3 (solid boundary, shade inside). Region more than 2m from fence: distance from fence > 2 (dashed boundary — point is NOT on the boundary, shade outside). Students annotate their diagrams with correct boundary type.
6. 6 A school wants to place a new building: it must be at least 20m from the sports hall, within 50m of the main entrance, and equidistant from two gates. Students mark the valid region using all three conditions.
7. 7 Present a completed loci diagram with three errors (wrong boundary type, wrong region shaded, locus drawn as a line when it should be a circle). Students identify and explain each error.

Tap a step to mark it as done.