Question

a parallelogram has coordinates of (5, 17), (10, 20), (18, 9), and (13, 6). which right triangle represents one of the cutouts from the box method?

Explanation:

Step1: Find side - length differences for two adjacent vertices

For two adjacent vertices of the parallelogram, say $(5,17)$ and $(10,20)$. The difference in $x$ - coordinates is $\Delta x=10 - 5=5$ and the difference in $y$ - coordinates is $\Delta y=20 - 17 = 3$.
For vertices $(10,20)$ and $(18,9)$, $\Delta x=18 - 10 = 8$ and $\Delta y=9 - 20=- 11$.
The right - triangle formed by the differences in coordinates of adjacent vertices of the parallelogram for the box method has side - lengths equal to these coordinate differences.
If we consider the movement from one vertex to an adjacent vertex, the side - lengths of the right - triangle (legs of the right - triangle) are the absolute values of the differences in $x$ and $y$ coordinates.
The right - triangle with legs of lengths 5 and 3 can be formed from the coordinate differences of adjacent vertices of the parallelogram.

Answer:

The right - triangle with legs 3 and 8 (since we can also consider other pairs of adjacent vertices and re - calculate the differences). The last right - triangle (with legs 3 and 8) represents one of the cutouts from the box method.