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.
Concept:
The figure shows three straight line segments that pass through a rectangular window WXYZ. Each of these three lines is visible outside the rectangle on both sides. Since every line is straight, the hidden piece inside the rectangle must be the exact continuation of each visible arm, with no bend and no change of direction at the boundary of the rectangle.
Step 1: Identify the three lines from their visible arms.
Two arms come from the top of the figure and cross each other above the rectangle before entering it, one arm entering close to corner W and the other close to corner X. On the outside below the rectangle, one steep arm leaves near corner Z and another steep arm leaves near corner Y. A third pair of arms leaves from the middle of the left side and the middle of the right side, running almost horizontally.
Step 2: Match each pair of arms into one straight line.
The arm entering near W keeps the same downward-to-the-right slope it had outside, so inside the rectangle it must continue down to the arm leaving near Y, giving one diagonal from the W corner region to the Y corner region.
The arm entering near X keeps its downward-to-the-left slope, so it must continue inside to meet the arm leaving near Z, giving the second diagonal from the X corner region to the Z corner region.
The two almost horizontal arms on the left and right sides belong to the third line, which must run nearly straight across the middle of the rectangle connecting them.
Step 3: Check each option for a straight, unbroken match.
In option P, the line meant to join the W side to Y and the line meant to join X to Z do not keep a constant slope matching the outside arms, and the near-horizontal line bends where it should stay straight.
In option Q, the two diagonal lines do not line up with the direction the outside arms are travelling in for one of the four corner regions.
In option R, the crossing point of the two diagonals sits too close to one corner instead of matching the position implied by the entry points of the outside arms, so at least one diagonal is off.
In option S, all three lines connect their correct pair of outside arms with a constant slope and no kink at the rectangle's boundary, exactly reproducing three uninterrupted straight lines.
Step 4: Final conclusion.
The missing portion WXYZ that keeps all three line segments straight is option S.
\[
\boxed{\text{S}}
\]
