Question

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.

Answer 1

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.