Skip to main content
### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Two Points Plus One Line

## You may also like

### Triangle Midpoints

### Pareq Exists

### The Medieval Octagon

Or search by topic

Age 14 to 16

Challenge Level

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

Well done Graham from Feilding High in New
Zealand and also to Andrei from Tudor Vianu National College,
Bucharest, who both gave good answers to the first part of the
problem.

The geometrical solution is to construct the perpendicular bisector of the line $AB$ and mark where it will cross the original line.

This solution works for all cases except where the line $AB$ is itself perpendicular to the original line AND the original line is not the perpendicular bisector of the line $AB$

Can someone now suggest parameters for the general arrangement so that any particular arrangement can be uniquely identified?

The geometrical solution is to construct the perpendicular bisector of the line $AB$ and mark where it will cross the original line.

This solution works for all cases except where the line $AB$ is itself perpendicular to the original line AND the original line is not the perpendicular bisector of the line $AB$

Can someone now suggest parameters for the general arrangement so that any particular arrangement can be uniquely identified?

You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

Prove that, given any three parallel lines, an equilateral triangle always exists with one vertex on each of the three lines.

Medieval stonemasons used a method to construct octagons using ruler and compasses... Is the octagon regular? Proof please.