Final answer:
The student's question is regarding the conditions for a quadrilateral formed by joining the midpoints of a given quadrilateral to be a rhombus. They ask which properties would ensure PQRS is a rhombus, and the answer lies in applying concepts similar to the parallelogram rule and vector addition used in physics and geometry.
Step-by-step explanation:
The student is asking about a property of a quadrilateral formed by joining the midpoints of the sides of another quadrilateral. To determine if the new quadrilateral, named PQRS, is a rhombus, several conditions can be considering, such as PQRS being a parallelogram, its diagonals being perpendicular, or its diagonals being equal.
Parallelogram rule and vector addition are often applied in physics to determine the resultant or difference of two vectors, which is conceptually similar to examining the properties of geometric shapes like parallelograms or rhombi. In geometry, especially when dealing with midpoints of sides, if PQRS is a parallelogram and its diagonals are equal, then PQRS would indeed be a rhombus.
The quadrilateral formed by joining the mid-points of the sides of a quadrilateral ABCD, taken in order, is a rhombus if the diagonals of PQRS are equal. This means that if the lengths of the diagonals PR and QS are equal, then the quadrilateral PQRS is a rhombus.