GATE CS 2021 Set 1 Q.2 (GA Q.2): Spatial Aptitude

A polygon is convex if, for every pair of points, $P$ and $Q$ belonging to the polygon, the line segment $PQ$ lies completely inside or on the polygon.

Which one of the following is NOT a convex polygon?

Concave chevron arrow-shaped polygon with an indented left vertex.

Official answer and solution

Official answer: A
From: Official GATE 2021 answer key

Solution

Check if a line segment connecting any two internal points can pass outside the polygon.

A polygon is convex if the straight line segment connecting any two points in the polygon lies entirely within or on the polygon. If there exists at least one pair of internal points such that their segment passes outside the polygon, the polygon is concave (non-convex).

Option A shows an arrowhead (chevron) shape having a reflex interior angle. Choosing one point on the left wing tip and another on the right wing tip results in a line segment that passes through the exterior empty space. Hence, option A is not a convex polygon.

Options B (triangle), C (square), and D (trapezoid) are all standard convex polygons where every interior angle is strictly less than $180^\circ$ .

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2021 Computer Science and Information Technology (CS, Set-1)
Question: 2 of 65, printed as GA Q.2
Section: General Aptitude

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