Let's plot the given points and draw the quadrilateral on a coordinate plane.
We can use the Slope Formula to determine whether the figure is a rectangle. Let's find the slope of each side.
Side
Slope Formula
Simplify
Slope of HG, ( - 7,7), ( 1,8)
8- 7/1-( - 7)
1/8
Slope of GK, ( 1,8), ( 2, 2)
2- 8/2- 1
- 6
Slope of JK, ( - 6, 1), ( 2, 2)
2- 1/2-( - 6)
1/8
Slope of HJ, ( - 7,7), ( - 6, 1)
1- 7/- 6-( - 7)
- 6
The slopes of the opposite sides of our quadrilateral are equal, so both pairs of opposite sides are parallel. Therefore, we know that the quadrilateral is a parallelogram. We can also tell that the consecutive side are not perpendicular, as their slopes are not opposite reciprocals.
- 6 * 1/8 ≠ -1
Therefore, our quadrilateral is not a rectangle, as its consecutive sides are not perpendicular.
