Quadrilateral DEFG has vertices D (-5, 9), E (-3, 6), F (-6, - 2), G (-8, 1). Determine if the quadrilateral is a parallelogram, rectangle, rhombus, or square.

Length of DE = sqrt ((-5 - - 3) ^2 + (9-6) ^2)) = sqrt 13

Length of the adjacent side EF = sqrt ((-3 - - 6) ^2 + (6 - - 2) ^2) = sqrt73

So its not a rhombus or a square.

Slope of DE = (9-6) / (-5 - -3) = - 3/2 and slope of EF = (6 - - 2) / (-3--6) = 8/3

these slope are not at right angles to each other

Therefore we haven't got a rectangle here.

Answer: - Parallelogram.