How to find perspectivity of the ranges on a line

Question

Question: Complete the perspectivity of the ranges on the lines $AB$ and $DF$ with centre $H$:
$ABF$ $\barwedge$ ?
I got $F$ as my first point but is lost after that. Need help. Also I was told to label my own lines on this picture

Answer 1

The perspectivity $AB\to DF$ of center $H$ sends $A\mapsto I$, where $I=AH\cap DF$, $B\mapsto E$ and $F\mapsto F$, thus you have to complete $ABF\barwedge IEF$.