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 JK, ( 0,7), ( - 8,6)
6- 7/- 8- 0
1/8
Slope of KL, ( - 8,6), ( - 7, 0)
0- 6/- 7-( - 8)
- 6
Slope of LM, ( - 7, 0), ( 1, 1)
1- 0/1-( -7)
1/8
Slope of MJ, ( 1,1), ( 0,7)
7- 1/0- 1
- 6
The slopes of opposite sides are equal. This means we have two pairs of parallel sides. Therefore, we know that the quadrilateral is in fact a parallelogram. However, we can also tell that consecutive sides are not perpendicular, because their slopes are not opposite reciprocals.
- 6 * 1/8 ≠-1
Therefore, our quadrilateral is not a rectangle, as it does not have four right angles.
