First we will verify that it is a trapezoid, and then we will determine whether the figure is an isosceles trapezoid.
Is It a Trapezoid?
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 JM: ( -4,-6), ( -4,- 4)
- 4-( -6)/-4-( -4)
undefined
Slope of ML: ( -4,- 1), ( 1, 3)
3-( - 1)/1-( -4)
4/5
Slope of LK: ( 1,3), ( 6, 2)
2- 3/6- 1
- 1/5
Slope of KJ: ( 6,2), ( -4,-6)
-6- 2/-4- 6
4/5
We can see that the slopes of JM and LK are not equal, so these sides are not parallel. The slopes of ML and KJ are equal, so these sides are parallel. Since our quadrilateral has exactly one pair of parallel sides, it is a trapezoid.
Is It an Isosceles Trapezoid?
A trapezoid is isosceles if its non-parallel sides are congruent. Therefore, we want to check whether the lengths of JM and LK are equal. To do this, we will use the Distance Formula.
Side
Distance Formula
Simplified
Length of JM: ( -4,-6), ( -4,- 4)
sqrt(( -4-( -4))^2+( - 4-( -6))^2)
2
Length of LK: ( 1,3), ( 6,2)
sqrt(( 6- 1)^2+( 2- 3)^2)
sqrt(26)
Since the lengths are not equal, legs JM and LK are not congruent. Therefore, KJML is not an isosceles trapezoid.
