Dividing a line segment into equal lengths
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In this exercise you given two points \(P\) and \(Q\) on a line. Your task is to construct points \(P_1, \ldots, P_{n-1}\) on this line such that \(|P_1| = |P_2| = \cdots = |P_{n-1} Q|\). In other words, your goal is to divide the line segment \(PQ\) into \(n\) equal lengths.
Hint. You will find Thales' theorem very useful!
The diagram contains an example of two points \(A\) and \(B\) on a line together with points \(A_1\) and \(A_2\) such that \(|A A_1| = |A_1 A_2| = |A_2 B|\), thus dividing the line segment \(AB\) into \(3\) equal lengths.
