Loci
Find every point at a given distance from a point, from a line segment, from two points or from the two arms of an angle, and see what shape they make. Then use compasses to shade a region that meets two conditions at once.
- UK: Year 9
- France: grade 2
- Germany: grade 7
- Iran: grade 10
- Syria: grade 7
- Palestine: grade 10
- Ukraine: grade 7
- Russia: grade 6
Guide
This studio is for Year 9 (KS3: the standard ruler and compass constructions, perpendicular distance and shortest distance). Iran teaches it in Year 10 geometry «ترسیمهای هندسی».
A locus is the set of all points with a given property. All the points 5 from a point O make a circle with centre O and radius 5, not a square. On a dotty grid, work out distances with Pythagoras' theorem; don't count steps along the grid.
The points 2 from a line segment make two lines parallel to it, joined by two semicircles at the ends. The distance from a point to a line is the shortest distance: along the perpendicular to the line, never on a slant.
The points the same distance from A and B are not just the midpoint of AB: every point on the perpendicular bisector of AB has this property. The points the same distance from the two arms of an angle lie on the angle bisector. Both are drawn with compasses and a ruler.