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Question:

Let P, Q, R, and S be the points on the plane with position vectors -i-j, 4i, 3i+3j, and 7i+2j respectively. The quadrilateral PQRS must be a rectangle, but not a square, rhombus, but not a square, parallelogram, which is neither a rhombus nor a rectangle.

square

rhombus, but not a square

parallelogram, which is neither a rhombus nor a rectangle

rectangle, but not a square

Solution:

Evaluating midpoint of PR and QS which gives M≡[i/2+j], same for both. →PQ=→SR=6i+j →PS=→QR=-i+3j