Let's begin by plotting the given vertices and drawing the quadrilateral on a coordinate plane.
To verify that our quadrilateral is a trapezoid, we have to check if our quadrilateral has exactly one pair of parallel sides. To do this, let's find the slope of each side using the Slope Formula.
Side
Slope Formula
Simplified
Slope of AB: ( -4,-1), ( -2,3)
3-( -1)/-2-( -4)
2
Slope of BC: ( - 2,3), ( 3, 3)
3- 3/3-( -2)
0
Slope of CD: ( 3,3), ( 5, - 1)
- 1- 3/5- 3
- 2
Slope of DA: ( 5, - 1), ( - 4,- 1)
-1-( - 1)/-4- 5
0
We can see that the slopes of AB and CD are not equal, so these sides are not parallel. The slopes of BC and DA are equal, so these sides are parallel. Since our quadrilateral has exactly one pair of parallel sides, it is a trapezoid.
