2024 CGSS P2 Q5

The diagram shows a line \(DE\) which cuts the \(y\)-axis at \(P\) and a line through \(F\) meets the \(y\)-axis at \(Q\) such that angle \(FPQ =\) angle \(FQP\).

The coordinates of \(D\) and \(E\) are \((-4, 0)\) and \((10, 7)\) respectively.

\(F\) is a point on the line \(DE\) such that \(DF : FE = 4 : 3\).

1. Find the coordinates of \(F\).[3]
2. Find the equation of the straight line \(FQ\).[2]
3. Find the area of the triangle \(QFE\).[3]