In a parallelogram, the pairs of opposite sides are parallel. Therefore, the quadrilateral is a parallelogram if opposite sides have the same slope. Let's use the Slope Formula to find the slope of each side.
Side
Slope Formula
Slope
Slope of AB: ( 2, 2),( 6, 4)
4- 2/6- 2
1/2
Slope of BC: ( 6, 4),( 8, 10)
10- 4/8- 6
3
Slope of CD: ( 8, 10),( 4, 8)
8- 10/4- 8
1/2
Slope of DA: ( 4, 8),( 2, 2)
2- 8/2- 4
3
The opposite sides in the quadrilateral have the same slope. Therefore, it is a parallelogram.
b A quadrilateral is a rectangle if adjacent sides are perpendicular. This would mean that their slopes would be negative reciprocals. Here, this is not the case.
1/2 * 3 ≠-1
Since the adjacent sides are not perpendicular, the quadrilateral is not a rectangle.
