Problem
GEO-B2-M07-P004 Common Base
#4
★★☆☆☆ Level 2 of 5
Points \(P\) and \(Q\) lie on the same side of line \(AB\). The distance from \(P\) to \(AB\) is \(3\) times the distance from \(Q\) to \(AB\). Find \([ABP]:[ABQ]\).
The triangles have common base \(AB\).
Triangles \(ABP\) and \(ABQ\) have common base \(AB\). Their areas are in the ratio of the altitudes to this base, hence \([ABP]:[ABQ]=3:1\).
Useful for problems with parallel lines.