Two fixed straight line $OX$ and $OY$ are cut by a variable line in the points $A$ and $B$ respectively and $P$ and $Q$ are the feet of the perpendiculars drawn from $A$ and $B$ upon the lines $OBY$ and $OAX$. Show that , if $AB$ passes through a fixed point, then $PQ$ will also pass through a fixed point.
Also make clear that what they mean by variable lines and fixed points/lines, means how to use them to solve this problem.
This is NOT a solution but a drawing to clarify what the question is asking.
OX and OY are two oblique axes. M is the said common fixed point, through which the variable lines (L) will pass. The solid blue line is one of the family. It cuts OX and OY at A and B respectively. Through A and B, perpendiculars (in light blue) are drawn to OBY and OAX at P and Q respectively. The line through PQ is in dotted blue.
Another two sets of lines (in red and in green) are drawn according to the same rule.
Note that the dotted lines will meet at one single point N. The question is asking - “is this true?”