Final answer:
The properties of parallelograms applied in this case are the parallelogram rule for vector addition, where the resultant and difference of vectors are represented by the diagonals of the parallelogram.
Step-by-step explanation:
The student is asking about the properties of parallelograms applied to solve vector problems in mathematics. To determine the values of x and y components of a vector, the property used is the parallelogram rule for vector addition. This rule states that when two vectors are represented as adjacent sides of a parallelogram, their resultant is represented by the diagonal of the parallelogram that starts from the common point of the two vectors. Similarly, the difference of the two vectors is represented by the other diagonal of the parallelogram. In a Cartesian coordinate system, vectors are often broken down into their x and y components, which are orthogonal projections of the vector onto the x-axis and y-axis. By applying the parallelogram rule and using these orthogonal components, we can solve for the resultant and difference of vectors.