Mathematics
Mathematics
Problem
The points P(1,2), Q(4,6), R(7,2) and S(4,-2) form a quadrilateral. Which of the following best describes quadrilateral PQRS? a) Square b) Parallelogram (not rhombus) c) Rhombus d) RectangleIntuitive explanation
The key is to check what makes this quadrilateral special by computing the side lengths and diagonals. A quadrilateral's properties—whether it's a parallelogram, rhombus, rectangle, or just a trapezoid—are revealed by symmetries in these distances. Calculate all four sides and both diagonals, then look for equal lengths or perpendicularity to identify the shape's defining characteristics.
Intuitive explanation
The key is to check what makes this quadrilateral special by computing the side lengths and diagonals. A quadrilateral's properties—whether it's a parallelogram, rhombus, rectangle, or just a trapezoid—are revealed by symmetries in these distances. Calculate all four sides and both diagonals, then look for equal lengths or perpendicularity to identify the shape's defining characteristics.