When you connect the points (1, 1), (4, 4), (7, 1), and (4, 2) on a coordinate plane, you will form a polygon. To analyze the shape, let’s briefly plot the points:
- Point A: (1, 1)
- Point B: (4, 4)
- Point C: (7, 1)
- Point D: (4, 2)
Next, we connect these points in the order A → B → C → D. Starting at point A (1, 1), we move to B (4, 4), which is higher up, then to C (7, 1), which is straight to the right on the same horizontal level as A, and finally to D (4, 2), which goes back to the left and slightly up. Plotting these points will reveal that the shape formed is a quadrilateral.
On closer examination, the quadrilateral is particularly interesting: it has one pair of parallel sides (the line segment connecting B to D and the segment connecting A to C). This indicates the shape is a trapezoid, since one pair of opposite sides is not parallel. Hence, the final shape formed is a trapezoid.