We can tell that the consecutive sides are not perpendicular, as their slopes are not opposite reciprocals.
- 2 * 0 ≠- 1
Since rectangles and squares have perpendicular sides, our parallelogram can only be rhombus or none of the given types of parallelograms. To check if it is a rhombus, we can find the lengths of its sides using the Distance Formula.
Side
Points
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Simplify
OP
O( 0,0), P( - 1,2)
sqrt(( - 1- 0)^2+( 2- 0)^2)
sqrt(5)
PT
P( - 1,2), T( 3, 2)
sqrt(( 3-( - 1))^2+( 2- 2)^2)
4
TS
T( 3, 2), S( 4, 0)
sqrt(( 4- 3)^2+( 0- 2)^2)
sqrt(5)
SO
S( 4, 0), O( 0,0)
sqrt(( 0- 4)^2+( 0- 0)^2)
4
Our parallelogram does not have four congruent sides. Therefore, the given parallelogram is not a rhombus and moreover it is none of the given types of parallelograms.
