The line fair to both ends
Two houses share one water pump. Where is the fair spot?
Step 1 of 4
- A segment, A to B.
- The same radius, an arc from A above and below the line.
- The same radius again, an arc from B. The arcs cross.
- Rule through the two crossings. Fair to both.
The perpendicular bisector
A fair spot is the same distance from both houses. All fair spots lie on one line.
Set the span to more than half of AB. Then the arcs cross. Strike arcs from A and from B with the same radius. They cross above AB and below it. Rule a line through both crossings.
That line meets AB at 90°. It divides AB into equal halves. This line is the perpendicular bisector of AB.
Points on the bisector are as far from A as from B. A point equally far from A and B lies on the bisector.
Example: AB is 60 mm. The middle is 60 ÷ 2 = 30 mm from each end. No point on the bisector is nearer to A than 30 mm.
Look at each point. Is it the same distance from A and B?
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