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?
Correct Answer :
Solution :
The correct option is S.
To determine which option correctly fills the missing rectangular portion WXYZ, we must analyze the entry and exit points, as well as the slopes, of the three line segments visible outside the rectangle in the main figure:
1. The horizontal-ish line (Line 1):
- A line segment with a small positive slope enters the left edge WZ (slightly below the midpoint) and exits the right edge XY (below the midpoint).
- This indicates that inside the missing rectangle, there must be a nearly horizontal line connecting the left side WZ to the right side XY.
2. The line with a negative slope (Line 2):
- A line segment enters the top edge WX on the left-middle side (around 1/3 of the distance from W) and is directed downwards and to the right (negative slope).
- On the outside bottom-right, we see a line segment aligned with this direction exiting near the bottom-right corner Y.
- Therefore, this line must connect the top edge WX to the bottom-right corner Y.
3. The line with a positive slope (Line 3):
- A line segment enters the bottom edge ZY on the left side (around 1/5 of the distance from Z) and is directed upwards and to the right (positive slope).
- On the top edge, another segment aligned with this slope exits on the right-middle side (around 2/3 of the distance from W).
- Therefore, this line must connect the bottom edge ZY to the top edge WX.
Now, let's evaluate the options P, Q, R, and S based on these connections:
- Option P: The line going from the bottom-left edge to the top edge (positive slope) does not align properly with the exit point at the top boundary WX. It ends too far to the left, which causes it to cross the negative-sloped line before reaching the top boundary.
- Option Q: Both diagonal lines have positive slopes, which is incorrect because one of the lines clearly has a negative slope.
- Option R: The positive-sloped line incorrectly terminates on the right edge XY instead of the top edge WX.
- Option S: All three lines correctly connect their respective entry and exit points: the nearly horizontal line goes from WZ to XY, the negative-sloped line goes from WX to Y, and the positive-sloped line goes from ZY to WX.
Hence, Option S is the correct missing portion of the figure.
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