We can use the Slope Formula to determine whether the figure is a rectangle. A rectangle is a type of parallelogram that has right angles. Let's first check if the figure is a parallelogram by finding the slope of each side.
Side
Slope Formula
Simplify
Slope of WX ( - 4,3), ( 1,5)
5- 3/1-( - 4)
2/5
Slope of XY ( 1,5), ( 3, 1)
1- 5/3- 1
- 2
Slope of YZ ( 3, 1), ( - 2, - 2)
- 2- 1/- 2- 3
3/5
Slope of ZW ( - 2, - 2), ( - 4,3)
3-( -2)/( - 4)-( - 2)
- 5/2
We can see that the slopes of the opposite sides of our quadrilateral are not equal, so both pairs of opposite sides are not parallel. Therefore, we know that the quadrilateral is not a parallelogram. We can also tell that consecutive sides are not perpendicular, as their slopes are not opposite reciprocals.
2/5 * (- 2) ≠-1 and 3/5 * ( - 5/2 ) ≠-1
Since our quadrilateral is not a parallelogram and its consecutive sides are not perpendicular, it cannot be a rectangle.
