We can tell that the slopes of the opposite sides of our quadrilateral are equal. Therefore, both pairs of opposite sides are parallel and the quadrilateral is therefore a parallelogram. We can also tell that the consecutive side are not perpendicular, as their slopes are not opposite reciprocals.
- 3 (2/3) ≠-1
Therefore, our quadrilateral is either a parallelogram or a rhombus. To check, we can find the lengths of its sides using the Distance Formula.
Side
Distance Formula
Simplified
Length of AB: ( - 1,4), ( 2,6)
sqrt(( 2-( - 1))^2+( 6- 4)^2)
sqrt(13)
Length of BC: ( 2,6), ( 3,3)
sqrt(( 3- 2)^2+( 3- 6)^2)
sqrt(10)
Length of CD: ( 3,3), ( 0,1)
sqrt(( 0- 3)^2+( 1- 3)^2)
sqrt(13)
Length of DA: ( 0,1), ( - 1,4)
sqrt(( - 1- 0)^2+( 4- 1)^2)
sqrt(10)
Our parallelogram has two pairs of congruent sides. Therefore, the most specific term for this quadrilateral is a parallelogram.
