Loci: choosing the construction
The Maths Habit
Which is the odd one out?
the same distance from A and B · exactly 3 m from the tree · the same distance from two walls · up to 5 km from the mast
Several answers: two are “the same distance”, two are from one thing.
- Equidistant
- The same distance from.
- Fixed distance
- A distance that does not change.
- Region
- The part of a drawing where every point fits a rule.
Find the rule. Is it from a point, a line, two points or two lines? Name the construction.
| From | a point | a line | two points | two lines |
|---|---|---|---|---|
| Locus | ||||
| Construction | circle | parallel lines, round ends | perpendicular bisector | angle bisector |
From what?
From what?
From what?
Which construction?
Which construction?
A tap must be the same distance from the gate G and the gate H.
Rulethe same distance from G and H
Fromtwo points
ConstructionPerpendicular bisector
A path stays the same distance from the two straight hedges that meet at C.
Rulethe same distance from two hedges
Fromtwo lines
ConstructionAngle bisector
A tap must be the same distance from the gate G and the gate H.
Rulethe same distance from G and H
Fromtwo points
ConstructionPerpendicular bisector
A goat is tied to a post P with a rope 4 m long. Show where it can reach.
Ruleup to 4 m from P
Froma point
ConstructionA circle
A tap must be the same distance from the gate G and the gate H.
Rulethe same distance from G and H
Fromtwo points
ConstructionPerpendicular bisector
A robot mower’s path is always exactly 1 m from the straight edge of the patio.
Ruleexactly 1 m from the edge
Froma line
ConstructionParallel lines, round ends
A tap must be the same distance from the gate G and the gate H.
Rulethe same distance from G and H
Fromtwo points
ConstructionPerpendicular bisector
A plant pot must be the same distance from the two walls that meet at the corner K.
Rulethe same distance from both walls
Fromtwo lines
ConstructionAngle bisector
A tap must be the same distance from the gate G and the gate H.
Rulethe same distance from G and H
Fromtwo points
ConstructionPerpendicular bisector
A phone mast is equidistant from the villages V and W.
Rulethe same distance from V and W
Fromtwo points
ConstructionPerpendicular bisector
“Less than”, “more than” and “nearer to”: what do they tell you to do after the construction?
Shade a region: inside or outside, or one side of the line.
Which side do you shade?
A bench is the same distance from the trees T and U, and less than 5 m from the pond P. Name both constructions.
Rule 1perpendicular bisector of TU
Rule 2circle about P, shade inside
The bus picks up everyone nearer to stop S than to stop R. Name the construction. Which side do you shade?
Constructionperpendicular bisector of SR
ShadeS's side
Answer sheet
Sort race: a point, a line, two points or two lines?
The same distance from the swings and the slide
two pointsWithin 50 m of the river bank
a lineNearer the north wall than the east wall
two linesExactly 2 km from the lighthouse
a pointEquidistant from three towns
two points, twice
A path runs the same distance from two parallel fences. Which construction finds it?
Bisect across the gapBen says “the same distance from” always means a perpendicular bisector. Give an example where it does not.
Two linesWrite a rule whose locus is a circle of radius 3 cm on a plan where 1 cm stands for 20 m.
60 m from a point
The same distance from two trees: which construction?
Perpendicular bisectorThe same distance from two walls that meet: which construction?
Angle bisectorUp to 4 m from a lamp, and nearer to A than B: which two constructions?
Circle and perpendicular bisector