The figure below has exactly three intersecting line segments with a rectangular portion WXYZ missing. Which one of the following options P, Q, R, and S is the missing portion WXYZ?
Show Hint
Each visible arm outside the rectangle must continue inside with exactly the same slope, since all three lines are straight.
Step 1: Label what a straight line demands.
A straight line cannot change direction. So for each of the three lines crossing the missing rectangle, the piece hidden inside must leave each side of the rectangle heading in exactly the same direction the visible arm outside is already heading.
Step 2: Look at the corners one at a time.
Near corner W and corner X at the top, two arms enter the rectangle after crossing each other above it. Near corner Z and corner Y at the bottom, two steep arms leave the rectangle. Reading the slopes, the arm at W must connect through to the arm at Y, and the arm at X must connect through to the arm at Z, since swapping this pairing would force a line to bend.
Step 3: Add the third, flatter line.
A nearly flat arm leaves the middle of the left edge, and a matching nearly flat arm leaves the middle of the right edge. Being almost horizontal, this third line has to travel close to straight across, only tilting slightly, to join these two side arms without a kink.
Step 4: Rule out P, Q, and R.
Checking each candidate rectangle against this plan, P and Q each show at least one diagonal that does not point toward the correct corner once you follow its slope from the visible arm, and R places the meeting point of its two diagonals too far toward one corner instead of centrally, so none of these three keep all three lines straight through the missing block.
Step 5: Confirm S.
Only the rectangle labelled S carries all three lines through with the same slope and position that the six visible outside arms demand, joining W to Y, X to Z, and the two side arms, all without a bend.
\[ \boxed{\text{S}} \]
