Geometry

Question Analysis:
This question involves identifying polygons based on vertices plotted on the coordinate plane.
The main focus is on classifying a polygon by analyzing side lengths and angles.

Key Concept Explanation:
A rectangle has four right angles and opposite sides that are equal and parallel.
A square has all properties of a rectangle plus all sides being equal in length.
A rhombus has all sides equal but not necessarily right angles.
A trapezoid has only one pair of parallel sides.

Step-by-Step Solution:
Plot the points (2, 3), (6, 3), (6, 7), (2, 7) or visualize their positions.
Find the lengths of the sides:
Between (2, 3) and (6, 3): horizontal distance = |6 - 2| = 4 units.
Between (6, 3) and (6, 7): vertical distance = |7 - 3| = 4 units.
Between (6, 7) and (2, 7): horizontal distance = |6 - 2| = 4 units.
Between (2, 7) and (2, 3): vertical distance = |7 - 3| = 4 units.
Check slopes to confirm right angles:
Slope between (2, 3) and (6, 3): (3 - 3)/(6 - 2) = 0 → horizontal line.
Slope between (6, 3) and (6, 7): (7 - 3)/(6 - 6) → undefined → vertical line.
Since adjacent sides are perpendicular (horizontal and vertical lines), each angle is 90°.
Check side lengths: all sides are 4 units long.
Since all sides are equal and all angles are 90°, this would suggest a square.