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Help: Dividing line with ratio

A segment \(PQ\) with \(2.1\) in length divided by point \(X\) so that \( \dfrac{PX}{XQ} = \dfrac{4}{3}\) and by point \(Y\) so that \(\dfrac{PY}{YQ} = -\dfrac{4}{3}\). Find \(XY\).

Note by Jason Chrysoprase
8 months ago

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We use the formulae for internal and external division of a line segment in a ratio:

If the division is \(\frac {m}{n}\) of segment \(AB\) and the internal point is \(C\) and the external point is \(D\), the internal length \(BC\) is \(\frac {n}{m+n} AB\) and the external length \(BD\) is \(\frac {n}{m-n}\).

Try to prove these formulae. We have

\(QX=\frac {3}{4+3} PQ \Rightarrow QX = 0.9\)

\(QY = \frac {3}{4-3} PQ \Rightarrow QY = 6.3\)

Thus, \(QX+QY=XY=7.2\). Sharky Kesa · 8 months ago

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