Final answer:
To find the fourth vertex of a parallelogram, one must use the properties of vectors and the parallelogram rule which states that the diagonals bisect each other. By drawing vectors between the given vertices, we can apply the rule to find the missing vertex ensuring that the opposite vectors are equal.
Step-by-step explanation:
The student's question involves finding the coordinates of the fourth vertex of a parallelogram given three of its vertices. To solve this, one must understand the properties of vectors and the parallelogram rule for vector addition. A parallelogram is a quadrilateral with opposite sides that are equal and parallel. The problem can be approached by considering the given vertices as points in a plane where two vectors can be formed from one vertex to the other two. The fourth vertex can be found by applying the parallelogram rule which states that the diagonals of a parallelogram bisect each other. Therefore, the midpoint of the diagonal between the given vertices will also be the midpoint of the diagonal between the missing vertex and the opposite vertex.
Step 1: Identify the vectors connected to the given vertices. Step 2: Use the parallelogram rule to determine the fourth vertex by finding the point that forms a parallelogram with the given points. By following the properties of a parallelogram, we can conclude the vectors connected to the opposite vertices are equal in magnitude and direction.