Final answer:
Upon reviewing the sets of points given, they are classified based on their geometric properties as a rectangle, trapezoid, square, and another rectangle.
Step-by-step explanation:
To classify the given sets of points into the most specific geometric figures when graphed on a coordinate grid, we need to consider the definitions of a square, rectangle, and trapezoid. A square is a quadrilateral with four equal sides and four right angles. A rectangle has four right angles, but opposite sides are equal (not necessarily all four sides). A trapezoid has at least one pair of parallel sides.
- (4, 1), (4, 5), (7, 5), (7, 1) - This set of points forms a rectangle because opposite sides are both equal and parallel, but the sides are not of equal length.
- (3, 2), (4, 5), (7, 5), (8, 2) - This set of points forms a trapezoid because it has only one pair of parallel sides, specifically (4, 5) to (7, 5) and (3, 2) to (8, 2) are non-parallel.
- (3, 4), (3, 6), (4, 6), (4, 4) - This set of points forms a square because all sides are equal and it has four right angles.
- (3, 4), (3, 6), (5, 6), (5, 4) - This set forms a rectangle as opposite sides are equal and it has four right angles, but the sides are not all of equal length like a square.
Therefore, the classification for each set of points is:
- a. Rectangle
- b. Trapezoid
- a. Square
- c. Rectangle