Finding the Fourth Vertex of a Parallelogram

This GeoGebra interactive worksheet demonstrates how to find all possible locations of the fourth vertex of a parallelogram given three coordinate points. The core mathematical concepts involved include the geometric properties of parallelograms (specifically that the diagonals bisect each other), vector addition, and coordinate geometry calculations. In terms of construction, the applet utilizes the `Random` command to generate three starting points, A, B, and C, then uses `Segment` and `Line` tools to draw the sides and construct parallel lines, finally applying the `Intersect` command to calculate the coordinates of the three potential fourth vertices, D, E, and F. This tool is highly suitable for secondary school students and teachers studying vector algebra and coordinate geometry, providing an excellent visual and practical exercise for understanding geometric transformations and vertex coordinates.