We can tell that consecutive sides are notperpendicular, as their slopes are notopposite reciprocals.
3 ( - 1/5 ) ≠-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
Points
d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
Simplify
QR
( - 2,- 1), ( - 1,2)
sqrt(( - 1-( - 2))^2+( 2-( -1))^2)
sqrt(10)
RS
( - 1,2), ( 4, 1)
sqrt(( 4-( - 1))^2+( 1- 2)^2)
sqrt(26)
ST
( 4, 1), ( 3, -2)
sqrt(( 3- 4)^2+( -2- 1)^2)
sqrt(10)
TQ
( 3, -2), ( - 2,-1)
sqrt(( - 2- 3)^2+( -1-( -2))^2)
sqrt(26)
Our quadrilateral has two pairs of sides of different lengths. Therefore, the most precise name for this quadrilateral is a parallelogram, then it's none of the mentioned.
